diff --git a/.github/workflows/test-suite.yml b/.github/workflows/test-suite.yml
index eb422e039..6c9b19d4f 100644
--- a/.github/workflows/test-suite.yml
+++ b/.github/workflows/test-suite.yml
@@ -115,6 +115,14 @@ jobs:
     - uses: actions/checkout@v1
     - name: Typecheck benchmark code without running it
       run: make check-benches
+  check-consensus:
+    name: check-consensus
+    runs-on: ubuntu-latest
+    needs: cargo-fmt
+    steps:
+    - uses: actions/checkout@v1
+    - name: Typecheck consensus code in strict mode
+      run: make check-consensus
   clippy:
     name: clippy
     runs-on: ubuntu-latest
diff --git a/Makefile b/Makefile
index 6fadf222f..39c2afaaa 100644
--- a/Makefile
+++ b/Makefile
@@ -93,6 +93,10 @@ cargo-fmt:
 check-benches:
 	cargo check --all --benches
 
+# Typechecks consensus code *without* allowing deprecated legacy arithmetic
+check-consensus:
+	cargo check --manifest-path=consensus/state_processing/Cargo.toml --no-default-features
+
 # Runs only the ef-test vectors.
 run-ef-tests:
 	cargo test --release --manifest-path=$(EF_TESTS)/Cargo.toml --features "ef_tests"
diff --git a/consensus/safe_arith/src/lib.rs b/consensus/safe_arith/src/lib.rs
index 227568210..ab5985a6e 100644
--- a/consensus/safe_arith/src/lib.rs
+++ b/consensus/safe_arith/src/lib.rs
@@ -28,24 +28,24 @@ macro_rules! assign_method {
 }
 
 /// Trait providing safe arithmetic operations for built-in types.
-pub trait SafeArith: Sized + Copy {
+pub trait SafeArith<Rhs = Self>: Sized + Copy {
     const ZERO: Self;
     const ONE: Self;
 
     /// Safe variant of `+` that guards against overflow.
-    fn safe_add(&self, other: Self) -> Result<Self>;
+    fn safe_add(&self, other: Rhs) -> Result<Self>;
 
     /// Safe variant of `-` that guards against overflow.
-    fn safe_sub(&self, other: Self) -> Result<Self>;
+    fn safe_sub(&self, other: Rhs) -> Result<Self>;
 
     /// Safe variant of `*` that guards against overflow.
-    fn safe_mul(&self, other: Self) -> Result<Self>;
+    fn safe_mul(&self, other: Rhs) -> Result<Self>;
 
     /// Safe variant of `/` that guards against division by 0.
-    fn safe_div(&self, other: Self) -> Result<Self>;
+    fn safe_div(&self, other: Rhs) -> Result<Self>;
 
     /// Safe variant of `%` that guards against division by 0.
-    fn safe_rem(&self, other: Self) -> Result<Self>;
+    fn safe_rem(&self, other: Rhs) -> Result<Self>;
 
     /// Safe variant of `<<` that guards against overflow.
     fn safe_shl(&self, other: u32) -> Result<Self>;
@@ -53,18 +53,13 @@ pub trait SafeArith: Sized + Copy {
     /// Safe variant of `>>` that guards against overflow.
     fn safe_shr(&self, other: u32) -> Result<Self>;
 
-    assign_method!(safe_add_assign, safe_add, "+=");
-    assign_method!(safe_sub_assign, safe_sub, "-=");
-    assign_method!(safe_mul_assign, safe_mul, "*=");
-    assign_method!(safe_div_assign, safe_div, "/=");
-    assign_method!(safe_rem_assign, safe_rem, "%=");
+    assign_method!(safe_add_assign, safe_add, Rhs, "+=");
+    assign_method!(safe_sub_assign, safe_sub, Rhs, "-=");
+    assign_method!(safe_mul_assign, safe_mul, Rhs, "*=");
+    assign_method!(safe_div_assign, safe_div, Rhs, "/=");
+    assign_method!(safe_rem_assign, safe_rem, Rhs, "%=");
     assign_method!(safe_shl_assign, safe_shl, u32, "<<=");
     assign_method!(safe_shr_assign, safe_shr, u32, ">>=");
-
-    /// Mutate `self` by adding 1, erroring on overflow.
-    fn increment(&mut self) -> Result<()> {
-        self.safe_add_assign(Self::ONE)
-    }
 }
 
 macro_rules! impl_safe_arith {
@@ -136,8 +131,7 @@ mod test {
     #[test]
     fn mutate() {
         let mut x = 0u8;
-        x.increment().unwrap();
-        x.increment().unwrap();
+        x.safe_add_assign(2).unwrap();
         assert_eq!(x, 2);
         x.safe_sub_assign(1).unwrap();
         assert_eq!(x, 1);
diff --git a/consensus/state_processing/Cargo.toml b/consensus/state_processing/Cargo.toml
index bae0705c8..bd0de6c19 100644
--- a/consensus/state_processing/Cargo.toml
+++ b/consensus/state_processing/Cargo.toml
@@ -27,14 +27,16 @@ log = "0.4.8"
 safe_arith = { path = "../safe_arith" }
 tree_hash = "0.1.0"
 tree_hash_derive = "0.2.0"
-types = { path = "../types" }
+types = { path = "../types", default-features = false }
 rayon = "1.3.0"
 eth2_hashing = "0.1.0"
 int_to_bytes = { path = "../int_to_bytes" }
 arbitrary = { version = "0.4.4", features = ["derive"], optional = true }
 
 [features]
+default = ["legacy-arith"]
 fake_crypto = ["bls/fake_crypto"]
+legacy-arith = ["types/legacy-arith"]
 arbitrary-fuzz = [
   "arbitrary",
   "types/arbitrary-fuzz",
diff --git a/consensus/state_processing/src/common/deposit_data_tree.rs b/consensus/state_processing/src/common/deposit_data_tree.rs
index 319c437ee..46f1ed8cc 100644
--- a/consensus/state_processing/src/common/deposit_data_tree.rs
+++ b/consensus/state_processing/src/common/deposit_data_tree.rs
@@ -47,7 +47,7 @@ impl DepositDataTree {
     /// Add a deposit to the merkle tree.
     pub fn push_leaf(&mut self, leaf: Hash256) -> Result<(), MerkleTreeError> {
         self.tree.push_leaf(leaf, self.depth)?;
-        self.mix_in_length.increment()?;
+        self.mix_in_length.safe_add_assign(1)?;
         Ok(())
     }
 }
diff --git a/consensus/state_processing/src/common/initiate_validator_exit.rs b/consensus/state_processing/src/common/initiate_validator_exit.rs
index 00cd02de1..3d2638a35 100644
--- a/consensus/state_processing/src/common/initiate_validator_exit.rs
+++ b/consensus/state_processing/src/common/initiate_validator_exit.rs
@@ -1,3 +1,4 @@
+use safe_arith::SafeArith;
 use std::cmp::max;
 use types::{BeaconStateError as Error, *};
 
@@ -22,7 +23,7 @@ pub fn initiate_validator_exit<T: EthSpec>(
     state.exit_cache.build(&state.validators, spec)?;
 
     // Compute exit queue epoch
-    let delayed_epoch = state.compute_activation_exit_epoch(state.current_epoch(), spec);
+    let delayed_epoch = state.compute_activation_exit_epoch(state.current_epoch(), spec)?;
     let mut exit_queue_epoch = state
         .exit_cache
         .max_epoch()?
@@ -30,13 +31,13 @@ pub fn initiate_validator_exit<T: EthSpec>(
     let exit_queue_churn = state.exit_cache.get_churn_at(exit_queue_epoch)?;
 
     if exit_queue_churn >= state.get_churn_limit(spec)? {
-        exit_queue_epoch += 1;
+        exit_queue_epoch.safe_add_assign(1)?;
     }
 
     state.exit_cache.record_validator_exit(exit_queue_epoch)?;
     state.validators[index].exit_epoch = exit_queue_epoch;
     state.validators[index].withdrawable_epoch =
-        exit_queue_epoch + spec.min_validator_withdrawability_delay;
+        exit_queue_epoch.safe_add(spec.min_validator_withdrawability_delay)?;
 
     Ok(())
 }
diff --git a/consensus/state_processing/src/common/slash_validator.rs b/consensus/state_processing/src/common/slash_validator.rs
index 754534f0c..0b0874819 100644
--- a/consensus/state_processing/src/common/slash_validator.rs
+++ b/consensus/state_processing/src/common/slash_validator.rs
@@ -23,7 +23,7 @@ pub fn slash_validator<T: EthSpec>(
     state.validators[slashed_index].slashed = true;
     state.validators[slashed_index].withdrawable_epoch = cmp::max(
         state.validators[slashed_index].withdrawable_epoch,
-        epoch + Epoch::from(T::EpochsPerSlashingsVector::to_u64()),
+        epoch.safe_add(T::EpochsPerSlashingsVector::to_u64())?,
     );
     let validator_effective_balance = state.get_effective_balance(slashed_index, spec)?;
     state.set_slashings(
diff --git a/consensus/state_processing/src/per_block_processing.rs b/consensus/state_processing/src/per_block_processing.rs
index 9bedba23e..e6c57beb2 100644
--- a/consensus/state_processing/src/per_block_processing.rs
+++ b/consensus/state_processing/src/per_block_processing.rs
@@ -368,7 +368,7 @@ pub fn process_attestations<T: EthSpec>(
         let pending_attestation = PendingAttestation {
             aggregation_bits: attestation.aggregation_bits.clone(),
             data: attestation.data.clone(),
-            inclusion_delay: (state.slot - attestation.data.slot).as_u64(),
+            inclusion_delay: state.slot.safe_sub(attestation.data.slot)?.as_u64(),
             proposer_index,
         };
 
@@ -444,7 +444,7 @@ pub fn process_deposit<T: EthSpec>(
             .map_err(|e| e.into_with_index(deposit_index))?;
     }
 
-    state.eth1_deposit_index.increment()?;
+    state.eth1_deposit_index.safe_add_assign(1)?;
 
     // Get an `Option<u64>` where `u64` is the validator index if this deposit public key
     // already exists in the beacon_state.
diff --git a/consensus/state_processing/src/per_block_processing/verify_attestation.rs b/consensus/state_processing/src/per_block_processing/verify_attestation.rs
index 3ab962e2e..678ba28e1 100644
--- a/consensus/state_processing/src/per_block_processing/verify_attestation.rs
+++ b/consensus/state_processing/src/per_block_processing/verify_attestation.rs
@@ -2,6 +2,7 @@ use super::errors::{AttestationInvalid as Invalid, BlockOperationError};
 use super::VerifySignatures;
 use crate::common::get_indexed_attestation;
 use crate::per_block_processing::is_valid_indexed_attestation;
+use safe_arith::SafeArith;
 use types::*;
 
 type Result<T> = std::result::Result<T, BlockOperationError<Invalid>>;
@@ -25,7 +26,7 @@ pub fn verify_attestation_for_block_inclusion<T: EthSpec>(
     let data = &attestation.data;
 
     verify!(
-        data.slot + spec.min_attestation_inclusion_delay <= state.slot,
+        data.slot.safe_add(spec.min_attestation_inclusion_delay)? <= state.slot,
         Invalid::IncludedTooEarly {
             state: state.slot,
             delay: spec.min_attestation_inclusion_delay,
@@ -33,7 +34,7 @@ pub fn verify_attestation_for_block_inclusion<T: EthSpec>(
         }
     );
     verify!(
-        state.slot <= data.slot + T::slots_per_epoch(),
+        state.slot <= data.slot.safe_add(T::slots_per_epoch())?,
         Invalid::IncludedTooLate {
             state: state.slot,
             attestation: data.slot,
diff --git a/consensus/state_processing/src/per_block_processing/verify_exit.rs b/consensus/state_processing/src/per_block_processing/verify_exit.rs
index c77ffe536..16c4db221 100644
--- a/consensus/state_processing/src/per_block_processing/verify_exit.rs
+++ b/consensus/state_processing/src/per_block_processing/verify_exit.rs
@@ -3,6 +3,7 @@ use crate::per_block_processing::{
     signature_sets::{exit_signature_set, get_pubkey_from_state},
     VerifySignatures,
 };
+use safe_arith::SafeArith;
 use types::*;
 
 type Result<T> = std::result::Result<T, BlockOperationError<ExitInvalid>>;
@@ -77,11 +78,14 @@ fn verify_exit_parametric<T: EthSpec>(
     );
 
     // Verify the validator has been active long enough.
+    let earliest_exit_epoch = validator
+        .activation_epoch
+        .safe_add(spec.shard_committee_period)?;
     verify!(
-        state.current_epoch() >= validator.activation_epoch + spec.shard_committee_period,
+        state.current_epoch() >= earliest_exit_epoch,
         ExitInvalid::TooYoungToExit {
             current_epoch: state.current_epoch(),
-            earliest_exit_epoch: validator.activation_epoch + spec.shard_committee_period,
+            earliest_exit_epoch,
         }
     );
 
diff --git a/consensus/state_processing/src/per_epoch_processing.rs b/consensus/state_processing/src/per_epoch_processing.rs
index 0321bce35..19b87aa57 100644
--- a/consensus/state_processing/src/per_epoch_processing.rs
+++ b/consensus/state_processing/src/per_epoch_processing.rs
@@ -84,7 +84,7 @@ pub fn process_justification_and_finalization<T: EthSpec>(
     state: &mut BeaconState<T>,
     total_balances: &TotalBalances,
 ) -> Result<(), Error> {
-    if state.current_epoch() <= T::genesis_epoch() + 1 {
+    if state.current_epoch() <= T::genesis_epoch().safe_add(1)? {
         return Ok(());
     }
 
@@ -126,25 +126,25 @@ pub fn process_justification_and_finalization<T: EthSpec>(
 
     // The 2nd/3rd/4th most recent epochs are all justified, the 2nd using the 4th as source.
     if (1..4).all(|i| bits.get(i).unwrap_or(false))
-        && old_previous_justified_checkpoint.epoch + 3 == current_epoch
+        && old_previous_justified_checkpoint.epoch.safe_add(3)? == current_epoch
     {
         state.finalized_checkpoint = old_previous_justified_checkpoint;
     }
     // The 2nd/3rd most recent epochs are both justified, the 2nd using the 3rd as source.
     else if (1..3).all(|i| bits.get(i).unwrap_or(false))
-        && old_previous_justified_checkpoint.epoch + 2 == current_epoch
+        && old_previous_justified_checkpoint.epoch.safe_add(2)? == current_epoch
     {
         state.finalized_checkpoint = old_previous_justified_checkpoint;
     }
     // The 1st/2nd/3rd most recent epochs are all justified, the 1st using the 3nd as source.
     if (0..3).all(|i| bits.get(i).unwrap_or(false))
-        && old_current_justified_checkpoint.epoch + 2 == current_epoch
+        && old_current_justified_checkpoint.epoch.safe_add(2)? == current_epoch
     {
         state.finalized_checkpoint = old_current_justified_checkpoint;
     }
     // The 1st/2nd most recent epochs are both justified, the 1st using the 2nd as source.
     else if (0..2).all(|i| bits.get(i).unwrap_or(false))
-        && old_current_justified_checkpoint.epoch + 1 == current_epoch
+        && old_current_justified_checkpoint.epoch.safe_add(1)? == current_epoch
     {
         state.finalized_checkpoint = old_current_justified_checkpoint;
     }
@@ -160,10 +160,15 @@ pub fn process_final_updates<T: EthSpec>(
     spec: &ChainSpec,
 ) -> Result<(), Error> {
     let current_epoch = state.current_epoch();
-    let next_epoch = state.next_epoch();
+    let next_epoch = state.next_epoch()?;
 
     // Reset eth1 data votes.
-    if (state.slot + 1) % T::SlotsPerEth1VotingPeriod::to_u64() == 0 {
+    if state
+        .slot
+        .safe_add(1)?
+        .safe_rem(T::SlotsPerEth1VotingPeriod::to_u64())?
+        == 0
+    {
         state.eth1_data_votes = VariableList::empty();
     }
 
diff --git a/consensus/state_processing/src/per_epoch_processing/apply_rewards.rs b/consensus/state_processing/src/per_epoch_processing/apply_rewards.rs
index 18c946520..4115bfef3 100644
--- a/consensus/state_processing/src/per_epoch_processing/apply_rewards.rs
+++ b/consensus/state_processing/src/per_epoch_processing/apply_rewards.rs
@@ -71,7 +71,10 @@ fn get_attestation_deltas<T: EthSpec>(
     validator_statuses: &ValidatorStatuses,
     spec: &ChainSpec,
 ) -> Result<Vec<Delta>, Error> {
-    let finality_delay = (state.previous_epoch() - state.finalized_checkpoint.epoch).as_u64();
+    let finality_delay = state
+        .previous_epoch()
+        .safe_sub(state.finalized_checkpoint.epoch)?
+        .as_u64();
 
     let mut deltas = vec![Delta::default(); state.validators.len()];
 
diff --git a/consensus/state_processing/src/per_epoch_processing/process_slashings.rs b/consensus/state_processing/src/per_epoch_processing/process_slashings.rs
index 4901d3030..4a8f8120d 100644
--- a/consensus/state_processing/src/per_epoch_processing/process_slashings.rs
+++ b/consensus/state_processing/src/per_epoch_processing/process_slashings.rs
@@ -14,7 +14,7 @@ pub fn process_slashings<T: EthSpec>(
 
     for (index, validator) in state.validators.iter().enumerate() {
         if validator.slashed
-            && epoch + T::EpochsPerSlashingsVector::to_u64().safe_div(2)?
+            && epoch.safe_add(T::EpochsPerSlashingsVector::to_u64().safe_div(2)?)?
                 == validator.withdrawable_epoch
         {
             let increment = spec.effective_balance_increment;
diff --git a/consensus/state_processing/src/per_epoch_processing/registry_updates.rs b/consensus/state_processing/src/per_epoch_processing/registry_updates.rs
index 79ece8c60..26f055ba4 100644
--- a/consensus/state_processing/src/per_epoch_processing/registry_updates.rs
+++ b/consensus/state_processing/src/per_epoch_processing/registry_updates.rs
@@ -1,6 +1,6 @@
-use super::super::common::initiate_validator_exit;
-use super::Error;
+use crate::{common::initiate_validator_exit, per_epoch_processing::Error};
 use itertools::Itertools;
+use safe_arith::SafeArith;
 use types::*;
 
 /// Performs a validator registry update, if required.
@@ -31,7 +31,7 @@ pub fn process_registry_updates<T: EthSpec>(
 
     for index in indices_to_update {
         if state.validators[index].is_eligible_for_activation_queue(spec) {
-            state.validators[index].activation_eligibility_epoch = current_epoch + 1;
+            state.validators[index].activation_eligibility_epoch = current_epoch.safe_add(1)?;
         }
         if is_ejectable(&state.validators[index]) {
             initiate_validator_exit(state, index, spec)?;
@@ -50,7 +50,7 @@ pub fn process_registry_updates<T: EthSpec>(
 
     // Dequeue validators for activation up to churn limit
     let churn_limit = state.get_churn_limit(spec)? as usize;
-    let delayed_activation_epoch = state.compute_activation_exit_epoch(current_epoch, spec);
+    let delayed_activation_epoch = state.compute_activation_exit_epoch(current_epoch, spec)?;
     for index in activation_queue.into_iter().take(churn_limit) {
         let validator = &mut state.validators[index];
         validator.activation_epoch = delayed_activation_epoch;
diff --git a/consensus/state_processing/src/per_slot_processing.rs b/consensus/state_processing/src/per_slot_processing.rs
index 02acfc825..a818bde52 100644
--- a/consensus/state_processing/src/per_slot_processing.rs
+++ b/consensus/state_processing/src/per_slot_processing.rs
@@ -1,10 +1,18 @@
 use crate::{per_epoch_processing::EpochProcessingSummary, *};
+use safe_arith::{ArithError, SafeArith};
 use types::*;
 
 #[derive(Debug, PartialEq)]
 pub enum Error {
     BeaconStateError(BeaconStateError),
     EpochProcessingError(EpochProcessingError),
+    ArithError(ArithError),
+}
+
+impl From<ArithError> for Error {
+    fn from(e: ArithError) -> Self {
+        Self::ArithError(e)
+    }
 }
 
 /// Advances a state forward by one slot, performing per-epoch processing if required.
@@ -21,14 +29,15 @@ pub fn per_slot_processing<T: EthSpec>(
 ) -> Result<Option<EpochProcessingSummary>, Error> {
     cache_state(state, state_root)?;
 
-    let summary = if state.slot > spec.genesis_slot && (state.slot + 1) % T::slots_per_epoch() == 0
+    let summary = if state.slot > spec.genesis_slot
+        && state.slot.safe_add(1)?.safe_rem(T::slots_per_epoch())? == 0
     {
         Some(per_epoch_processing(state, spec)?)
     } else {
         None
     };
 
-    state.slot += 1;
+    state.slot.safe_add_assign(1)?;
 
     Ok(summary)
 }
@@ -48,7 +57,7 @@ fn cache_state<T: EthSpec>(
     //
     // This is a bit hacky, however it gets the job safely without lots of code.
     let previous_slot = state.slot;
-    state.slot += 1;
+    state.slot.safe_add_assign(1)?;
 
     // Store the previous slot's post state transition root.
     state.set_state_root(previous_slot, previous_state_root)?;
@@ -63,7 +72,7 @@ fn cache_state<T: EthSpec>(
     state.set_block_root(previous_slot, latest_block_root)?;
 
     // Set the state slot back to what it should be.
-    state.slot -= 1;
+    state.slot.safe_sub_assign(1)?;
 
     Ok(())
 }
diff --git a/consensus/types/Cargo.toml b/consensus/types/Cargo.toml
index d893ff3ad..8f6fed4b4 100644
--- a/consensus/types/Cargo.toml
+++ b/consensus/types/Cargo.toml
@@ -46,7 +46,9 @@ serde_json = "1.0.52"
 criterion = "0.3.2"
 
 [features]
-default = ["sqlite"]
+default = ["sqlite", "legacy-arith"]
+# Allow saturating arithmetic on slots and epochs. Enabled by default, but deprecated.
+legacy-arith = []
 sqlite = ["rusqlite"]
 arbitrary-fuzz = [
   "arbitrary",
diff --git a/consensus/types/src/beacon_state.rs b/consensus/types/src/beacon_state.rs
index a335d0492..a2d923da9 100644
--- a/consensus/types/src/beacon_state.rs
+++ b/consensus/types/src/beacon_state.rs
@@ -100,10 +100,10 @@ enum AllowNextEpoch {
 }
 
 impl AllowNextEpoch {
-    fn upper_bound_of(self, current_epoch: Epoch) -> Epoch {
+    fn upper_bound_of(self, current_epoch: Epoch) -> Result<Epoch, Error> {
         match self {
-            AllowNextEpoch::True => current_epoch + 1,
-            AllowNextEpoch::False => current_epoch,
+            AllowNextEpoch::True => Ok(current_epoch.safe_add(1)?),
+            AllowNextEpoch::False => Ok(current_epoch),
         }
     }
 }
@@ -323,7 +323,9 @@ impl<T: EthSpec> BeaconState<T> {
     pub fn previous_epoch(&self) -> Epoch {
         let current_epoch = self.current_epoch();
         if current_epoch > T::genesis_epoch() {
-            current_epoch - 1
+            current_epoch
+                .safe_sub(1)
+                .expect("current epoch greater than genesis implies greater than 0")
         } else {
             current_epoch
         }
@@ -332,8 +334,8 @@ impl<T: EthSpec> BeaconState<T> {
     /// The epoch following `self.current_epoch()`.
     ///
     /// Spec v0.12.1
-    pub fn next_epoch(&self) -> Epoch {
-        self.current_epoch() + 1
+    pub fn next_epoch(&self) -> Result<Epoch, Error> {
+        Ok(self.current_epoch().safe_add(1)?)
     }
 
     /// Compute the number of committees at `slot`.
@@ -378,7 +380,7 @@ impl<T: EthSpec> BeaconState<T> {
         epoch: Epoch,
         spec: &ChainSpec,
     ) -> Result<Vec<usize>, Error> {
-        if epoch >= self.compute_activation_exit_epoch(self.current_epoch(), spec) {
+        if epoch >= self.compute_activation_exit_epoch(self.current_epoch(), spec)? {
             Err(BeaconStateError::EpochOutOfBounds)
         } else {
             Ok(get_active_validator_indices(&self.validators, epoch))
@@ -475,7 +477,7 @@ impl<T: EthSpec> BeaconState<T> {
             {
                 return Ok(candidate_index);
             }
-            i.increment()?;
+            i.safe_add_assign(1)?;
         }
     }
 
@@ -553,7 +555,7 @@ impl<T: EthSpec> BeaconState<T> {
     ///
     /// Spec v0.12.1
     fn get_latest_block_roots_index(&self, slot: Slot) -> Result<usize, Error> {
-        if slot < self.slot && self.slot <= slot + self.block_roots.len() as u64 {
+        if slot < self.slot && self.slot <= slot.safe_add(self.block_roots.len() as u64)? {
             Ok(slot.as_usize().safe_rem(self.block_roots.len())?)
         } else {
             Err(BeaconStateError::SlotOutOfBounds)
@@ -605,7 +607,9 @@ impl<T: EthSpec> BeaconState<T> {
         let current_epoch = self.current_epoch();
         let len = T::EpochsPerHistoricalVector::to_u64();
 
-        if current_epoch < epoch + len && epoch <= allow_next_epoch.upper_bound_of(current_epoch) {
+        if current_epoch < epoch.safe_add(len)?
+            && epoch <= allow_next_epoch.upper_bound_of(current_epoch)?
+        {
             Ok(epoch.as_usize().safe_rem(len as usize)?)
         } else {
             Err(Error::EpochOutOfBounds)
@@ -652,7 +656,7 @@ impl<T: EthSpec> BeaconState<T> {
     ///
     /// Spec v0.12.1
     fn get_latest_state_roots_index(&self, slot: Slot) -> Result<usize, Error> {
-        if slot < self.slot && self.slot <= slot + self.state_roots.len() as u64 {
+        if slot < self.slot && self.slot <= slot.safe_add(self.state_roots.len() as u64)? {
             Ok(slot.as_usize().safe_rem(self.state_roots.len())?)
         } else {
             Err(BeaconStateError::SlotOutOfBounds)
@@ -672,7 +676,7 @@ impl<T: EthSpec> BeaconState<T> {
     /// Spec v0.12.1
     pub fn get_oldest_state_root(&self) -> Result<&Hash256, Error> {
         let i =
-            self.get_latest_state_roots_index(self.slot - Slot::from(self.state_roots.len()))?;
+            self.get_latest_state_roots_index(self.slot.saturating_sub(self.state_roots.len()))?;
         Ok(&self.state_roots[i])
     }
 
@@ -680,7 +684,9 @@ impl<T: EthSpec> BeaconState<T> {
     ///
     /// Spec v0.12.1
     pub fn get_oldest_block_root(&self) -> Result<&Hash256, Error> {
-        let i = self.get_latest_block_roots_index(self.slot - self.block_roots.len() as u64)?;
+        let i = self.get_latest_block_roots_index(
+            self.slot.saturating_sub(self.block_roots.len() as u64),
+        )?;
         Ok(&self.block_roots[i])
     }
 
@@ -712,8 +718,8 @@ impl<T: EthSpec> BeaconState<T> {
         // We allow the slashings vector to be accessed at any cached epoch at or before
         // the current epoch, or the next epoch if `AllowNextEpoch::True` is passed.
         let current_epoch = self.current_epoch();
-        if current_epoch < epoch + T::EpochsPerSlashingsVector::to_u64()
-            && epoch <= allow_next_epoch.upper_bound_of(current_epoch)
+        if current_epoch < epoch.safe_add(T::EpochsPerSlashingsVector::to_u64())?
+            && epoch <= allow_next_epoch.upper_bound_of(current_epoch)?
         {
             Ok(epoch
                 .as_usize()
@@ -775,7 +781,10 @@ impl<T: EthSpec> BeaconState<T> {
         // Bypass the safe getter for RANDAO so we can gracefully handle the scenario where `epoch
         // == 0`.
         let mix = {
-            let i = epoch + T::EpochsPerHistoricalVector::to_u64() - spec.min_seed_lookahead - 1;
+            let i = epoch
+                .safe_add(T::EpochsPerHistoricalVector::to_u64())?
+                .safe_sub(spec.min_seed_lookahead)?
+                .safe_sub(1)?;
             self.randao_mixes[i.as_usize().safe_rem(self.randao_mixes.len())?]
         };
         let domain_bytes = int_to_bytes4(spec.get_domain_constant(domain_type));
@@ -811,8 +820,12 @@ impl<T: EthSpec> BeaconState<T> {
     ///  Return the epoch at which an activation or exit triggered in ``epoch`` takes effect.
     ///
     ///  Spec v0.12.1
-    pub fn compute_activation_exit_epoch(&self, epoch: Epoch, spec: &ChainSpec) -> Epoch {
-        epoch + 1 + spec.max_seed_lookahead
+    pub fn compute_activation_exit_epoch(
+        &self,
+        epoch: Epoch,
+        spec: &ChainSpec,
+    ) -> Result<Epoch, Error> {
+        Ok(epoch.safe_add(1)?.safe_add(spec.max_seed_lookahead)?)
     }
 
     /// Return the churn limit for the current epoch (number of validators who can leave per epoch).
diff --git a/consensus/types/src/beacon_state/committee_cache.rs b/consensus/types/src/beacon_state/committee_cache.rs
index f71ad2e89..6ee24cd2b 100644
--- a/consensus/types/src/beacon_state/committee_cache.rs
+++ b/consensus/types/src/beacon_state/committee_cache.rs
@@ -3,6 +3,7 @@
 use super::BeaconState;
 use crate::*;
 use core::num::NonZeroUsize;
+use safe_arith::SafeArith;
 use serde_derive::{Deserialize, Serialize};
 use ssz_derive::{Decode, Encode};
 use std::ops::Range;
@@ -197,7 +198,7 @@ impl CommitteeCache {
         let epoch_start_slot = self.initialized_epoch?.start_slot(self.slots_per_epoch);
         let slot_offset = global_committee_index / self.committees_per_slot;
         let index = global_committee_index % self.committees_per_slot;
-        Some((epoch_start_slot + slot_offset, index))
+        Some((epoch_start_slot.safe_add(slot_offset).ok()?, index))
     }
 
     /// Returns the number of active validators in the initialized epoch.
diff --git a/consensus/types/src/beacon_state/committee_cache/tests.rs b/consensus/types/src/beacon_state/committee_cache/tests.rs
index ee2ca8eed..e1256cb48 100644
--- a/consensus/types/src/beacon_state/committee_cache/tests.rs
+++ b/consensus/types/src/beacon_state/committee_cache/tests.rs
@@ -53,8 +53,8 @@ fn initializes_with_the_right_epoch() {
     let cache = CommitteeCache::initialized(&state, state.previous_epoch(), &spec).unwrap();
     assert_eq!(cache.initialized_epoch, Some(state.previous_epoch()));
 
-    let cache = CommitteeCache::initialized(&state, state.next_epoch(), &spec).unwrap();
-    assert_eq!(cache.initialized_epoch, Some(state.next_epoch()));
+    let cache = CommitteeCache::initialized(&state, state.next_epoch().unwrap(), &spec).unwrap();
+    assert_eq!(cache.initialized_epoch, Some(state.next_epoch().unwrap()));
 }
 
 #[test]
@@ -81,7 +81,7 @@ fn shuffles_for_the_right_epoch() {
         .get_seed(state.current_epoch(), Domain::BeaconAttester, spec)
         .unwrap();
     let next_seed = state
-        .get_seed(state.next_epoch(), Domain::BeaconAttester, spec)
+        .get_seed(state.next_epoch().unwrap(), Domain::BeaconAttester, spec)
         .unwrap();
 
     assert!((previous_seed != current_seed) && (current_seed != next_seed));
@@ -114,7 +114,7 @@ fn shuffles_for_the_right_epoch() {
     assert_eq!(cache.shuffling, shuffling_with_seed(previous_seed));
     assert_shuffling_positions_accurate(&cache);
 
-    let cache = CommitteeCache::initialized(&state, state.next_epoch(), spec).unwrap();
+    let cache = CommitteeCache::initialized(&state, state.next_epoch().unwrap(), spec).unwrap();
     assert_eq!(cache.shuffling, shuffling_with_seed(next_seed));
     assert_shuffling_positions_accurate(&cache);
 }
diff --git a/consensus/types/src/beacon_state/exit_cache.rs b/consensus/types/src/beacon_state/exit_cache.rs
index 0f75e0f28..364c1daf0 100644
--- a/consensus/types/src/beacon_state/exit_cache.rs
+++ b/consensus/types/src/beacon_state/exit_cache.rs
@@ -44,7 +44,7 @@ impl ExitCache {
         self.exit_epoch_counts
             .entry(exit_epoch)
             .or_insert(0)
-            .increment()?;
+            .safe_add_assign(1)?;
         Ok(())
     }
 
diff --git a/consensus/types/src/relative_epoch.rs b/consensus/types/src/relative_epoch.rs
index 381f17308..e681ce15c 100644
--- a/consensus/types/src/relative_epoch.rs
+++ b/consensus/types/src/relative_epoch.rs
@@ -1,9 +1,17 @@
 use crate::*;
+use safe_arith::{ArithError, SafeArith};
 
 #[derive(Debug, PartialEq, Clone, Copy)]
 pub enum Error {
     EpochTooLow { base: Epoch, other: Epoch },
     EpochTooHigh { base: Epoch, other: Epoch },
+    ArithError(ArithError),
+}
+
+impl From<ArithError> for Error {
+    fn from(e: ArithError) -> Self {
+        Self::ArithError(e)
+    }
 }
 
 #[cfg(feature = "arbitrary-fuzz")]
@@ -32,8 +40,8 @@ impl RelativeEpoch {
         match self {
             // Due to saturating nature of epoch, check for current first.
             RelativeEpoch::Current => base,
-            RelativeEpoch::Previous => base - 1,
-            RelativeEpoch::Next => base + 1,
+            RelativeEpoch::Previous => base.saturating_sub(1u64),
+            RelativeEpoch::Next => base.saturating_add(1u64),
         }
     }
 
@@ -46,12 +54,11 @@ impl RelativeEpoch {
     ///
     /// Spec v0.12.1
     pub fn from_epoch(base: Epoch, other: Epoch) -> Result<Self, Error> {
-        // Due to saturating nature of epoch, check for current first.
         if other == base {
             Ok(RelativeEpoch::Current)
-        } else if other == base - 1 {
+        } else if other.safe_add(1)? == base {
             Ok(RelativeEpoch::Previous)
-        } else if other == base + 1 {
+        } else if other == base.safe_add(1)? {
             Ok(RelativeEpoch::Next)
         } else if other < base {
             Err(Error::EpochTooLow { base, other })
diff --git a/consensus/types/src/slot_epoch.rs b/consensus/types/src/slot_epoch.rs
index ea4e23375..ffb88c7ee 100644
--- a/consensus/types/src/slot_epoch.rs
+++ b/consensus/types/src/slot_epoch.rs
@@ -14,21 +14,23 @@ use crate::test_utils::TestRandom;
 use crate::SignedRoot;
 
 use rand::RngCore;
+use safe_arith::SafeArith;
 use serde_derive::{Deserialize, Serialize};
 use ssz::{ssz_encode, Decode, DecodeError, Encode};
-use std::cmp::{Ord, Ordering};
 use std::fmt;
-use std::hash::{Hash, Hasher};
+use std::hash::Hash;
 use std::iter::Iterator;
+
+#[cfg(feature = "legacy-arith")]
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Rem, Sub, SubAssign};
 
 #[cfg_attr(feature = "arbitrary-fuzz", derive(arbitrary::Arbitrary))]
-#[derive(Eq, Clone, Copy, Default, Serialize, Deserialize)]
+#[derive(Clone, Copy, Default, PartialEq, Eq, PartialOrd, Ord, Hash, Serialize, Deserialize)]
 #[serde(transparent)]
 pub struct Slot(u64);
 
 #[cfg_attr(feature = "arbitrary-fuzz", derive(arbitrary::Arbitrary))]
-#[derive(Eq, Clone, Copy, Default, Serialize, Deserialize)]
+#[derive(Clone, Copy, Default, PartialEq, Eq, PartialOrd, Ord, Hash, Serialize, Deserialize)]
 #[serde(transparent)]
 pub struct Epoch(u64);
 
@@ -41,7 +43,9 @@ impl Slot {
     }
 
     pub fn epoch(self, slots_per_epoch: u64) -> Epoch {
-        Epoch::from(self.0) / Epoch::from(slots_per_epoch)
+        Epoch::new(self.0)
+            .safe_div(slots_per_epoch)
+            .expect("slots_per_epoch is not 0")
     }
 
     pub fn max_value() -> Slot {
@@ -96,9 +100,6 @@ impl Epoch {
     }
 }
 
-impl SignedRoot for Epoch {}
-impl SignedRoot for Slot {}
-
 pub struct SlotIter<'a> {
     current_iteration: u64,
     epoch: &'a Epoch,
@@ -115,7 +116,7 @@ impl<'a> Iterator for SlotIter<'a> {
             let start_slot = self.epoch.start_slot(self.slots_per_epoch);
             let previous = self.current_iteration;
             self.current_iteration = self.current_iteration.checked_add(1)?;
-            Some(start_slot + previous)
+            start_slot.safe_add(previous).ok()
         }
     }
 }
diff --git a/consensus/types/src/slot_epoch_macros.rs b/consensus/types/src/slot_epoch_macros.rs
index 15263f654..26b80692c 100644
--- a/consensus/types/src/slot_epoch_macros.rs
+++ b/consensus/types/src/slot_epoch_macros.rs
@@ -42,22 +42,84 @@ macro_rules! impl_from_into_usize {
     };
 }
 
+macro_rules! impl_u64_eq_ord {
+    ($type: ident) => {
+        impl PartialEq<u64> for $type {
+            fn eq(&self, other: &u64) -> bool {
+                self.as_u64() == *other
+            }
+        }
+
+        impl PartialOrd<u64> for $type {
+            fn partial_cmp(&self, other: &u64) -> Option<std::cmp::Ordering> {
+                self.as_u64().partial_cmp(other)
+            }
+        }
+    };
+}
+
+macro_rules! impl_safe_arith {
+    ($type: ident, $rhs_ty: ident) => {
+        impl safe_arith::SafeArith<$rhs_ty> for $type {
+            const ZERO: Self = $type::new(0);
+            const ONE: Self = $type::new(1);
+
+            fn safe_add(&self, other: $rhs_ty) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_add(other.into())
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::Overflow)
+            }
+
+            fn safe_sub(&self, other: $rhs_ty) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_sub(other.into())
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::Overflow)
+            }
+
+            fn safe_mul(&self, other: $rhs_ty) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_mul(other.into())
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::Overflow)
+            }
+
+            fn safe_div(&self, other: $rhs_ty) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_div(other.into())
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::DivisionByZero)
+            }
+
+            fn safe_rem(&self, other: $rhs_ty) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_rem(other.into())
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::DivisionByZero)
+            }
+
+            fn safe_shl(&self, other: u32) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_shl(other)
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::Overflow)
+            }
+
+            fn safe_shr(&self, other: u32) -> safe_arith::Result<Self> {
+                self.0
+                    .checked_shr(other)
+                    .map(Self::new)
+                    .ok_or(safe_arith::ArithError::Overflow)
+            }
+        }
+    };
+}
+
+// Deprecated: prefer `SafeArith` methods for new code.
+#[cfg(feature = "legacy-arith")]
 macro_rules! impl_math_between {
     ($main: ident, $other: ident) => {
-        impl PartialOrd<$other> for $main {
-            /// Utilizes `partial_cmp` on the underlying `u64`.
-            fn partial_cmp(&self, other: &$other) -> Option<Ordering> {
-                Some(self.0.cmp(&(*other).into()))
-            }
-        }
-
-        impl PartialEq<$other> for $main {
-            fn eq(&self, other: &$other) -> bool {
-                let other: u64 = (*other).into();
-                self.0 == other
-            }
-        }
-
         impl Add<$other> for $main {
             type Output = $main;
 
@@ -144,33 +206,17 @@ macro_rules! impl_math {
     ($type: ident) => {
         impl $type {
             pub fn saturating_sub<T: Into<$type>>(&self, other: T) -> $type {
-                *self - other.into()
+                $type::new(self.as_u64().saturating_sub(other.into().as_u64()))
             }
 
             pub fn saturating_add<T: Into<$type>>(&self, other: T) -> $type {
-                *self + other.into()
-            }
-
-            pub fn checked_div<T: Into<$type>>(&self, rhs: T) -> Option<$type> {
-                let rhs: $type = rhs.into();
-                if rhs == 0 {
-                    None
-                } else {
-                    Some(*self / rhs)
-                }
+                $type::new(self.as_u64().saturating_add(other.into().as_u64()))
             }
 
             pub fn is_power_of_two(&self) -> bool {
                 self.0.is_power_of_two()
             }
         }
-
-        impl Ord for $type {
-            fn cmp(&self, other: &$type) -> Ordering {
-                let other: u64 = (*other).into();
-                self.0.cmp(&other)
-            }
-        }
     };
 }
 
@@ -257,6 +303,8 @@ macro_rules! impl_ssz {
             }
         }
 
+        impl SignedRoot for $type {}
+
         impl TestRandom for $type {
             fn random_for_test(rng: &mut impl RngCore) -> Self {
                 $type::from(u64::random_for_test(rng))
@@ -265,29 +313,21 @@ macro_rules! impl_ssz {
     };
 }
 
-macro_rules! impl_hash {
-    ($type: ident) => {
-        // Implemented to stop clippy lint:
-        // https://rust-lang.github.io/rust-clippy/master/index.html#derive_hash_xor_eq
-        impl Hash for $type {
-            fn hash<H: Hasher>(&self, state: &mut H) {
-                ssz_encode(self).hash(state)
-            }
-        }
-    };
-}
-
 macro_rules! impl_common {
     ($type: ident) => {
         impl_from_into_u64!($type);
         impl_from_into_usize!($type);
+        impl_u64_eq_ord!($type);
+        impl_safe_arith!($type, $type);
+        impl_safe_arith!($type, u64);
+        #[cfg(feature = "legacy-arith")]
         impl_math_between!($type, $type);
+        #[cfg(feature = "legacy-arith")]
         impl_math_between!($type, u64);
         impl_math!($type);
         impl_display!($type);
         impl_debug!($type);
         impl_ssz!($type);
-        impl_hash!($type);
     };
 }
 
@@ -335,6 +375,7 @@ macro_rules! math_between_tests {
     ($type: ident, $other: ident) => {
         #[test]
         fn partial_ord() {
+            use std::cmp::Ordering;
             let assert_partial_ord = |a: u64, partial_ord: Ordering, b: u64| {
                 let other: $other = $type(b).into();
                 assert_eq!($type(a).partial_cmp(&other), Some(partial_ord));
@@ -518,7 +559,7 @@ macro_rules! math_tests {
         #[test]
         fn checked_div() {
             let assert_checked_div = |a: u64, b: u64, result: Option<u64>| {
-                let division_result_as_u64 = match $type(a).checked_div($type(b)) {
+                let division_result_as_u64 = match $type(a).safe_div($type(b)).ok() {
                     None => None,
                     Some(val) => Some(val.as_u64()),
                 };
@@ -560,6 +601,7 @@ macro_rules! math_tests {
 
         #[test]
         fn ord() {
+            use std::cmp::Ordering;
             let assert_ord = |a: u64, ord: Ordering, b: u64| {
                 assert_eq!($type(a).cmp(&$type(b)), ord);
             };
diff --git a/consensus/types/src/test_utils/builders/testing_attestation_data_builder.rs b/consensus/types/src/test_utils/builders/testing_attestation_data_builder.rs
index 9ecef2815..56b3e3bbe 100644
--- a/consensus/types/src/test_utils/builders/testing_attestation_data_builder.rs
+++ b/consensus/types/src/test_utils/builders/testing_attestation_data_builder.rs
@@ -1,5 +1,6 @@
 use crate::test_utils::AttestationTestTask;
 use crate::*;
+use safe_arith::SafeArith;
 
 /// Builds an `AttestationData` to be used for testing purposes.
 ///
@@ -49,12 +50,19 @@ impl TestingAttestationDataBuilder {
 
         match test_task {
             AttestationTestTask::IncludedTooEarly => {
-                slot = state.slot - spec.min_attestation_inclusion_delay + 1
+                slot = state
+                    .slot
+                    .safe_sub(spec.min_attestation_inclusion_delay)
+                    .unwrap()
+                    .safe_add(1u64)
+                    .unwrap();
             }
-            AttestationTestTask::IncludedTooLate => slot -= T::SlotsPerEpoch::to_u64(),
+            AttestationTestTask::IncludedTooLate => slot
+                .safe_sub_assign(Slot::new(T::SlotsPerEpoch::to_u64()))
+                .unwrap(),
             AttestationTestTask::TargetEpochSlotMismatch => {
                 target = Checkpoint {
-                    epoch: current_epoch + 1,
+                    epoch: current_epoch.safe_add(1u64).unwrap(),
                     root: Hash256::zero(),
                 };
                 assert_ne!(target.epoch, slot.epoch(T::slots_per_epoch()));
diff --git a/consensus/types/src/test_utils/builders/testing_beacon_block_builder.rs b/consensus/types/src/test_utils/builders/testing_beacon_block_builder.rs
index c396d8c96..97fe62780 100644
--- a/consensus/types/src/test_utils/builders/testing_beacon_block_builder.rs
+++ b/consensus/types/src/test_utils/builders/testing_beacon_block_builder.rs
@@ -9,6 +9,7 @@ use crate::{
 use int_to_bytes::int_to_bytes32;
 use merkle_proof::MerkleTree;
 use rayon::prelude::*;
+use safe_arith::SafeArith;
 use tree_hash::TreeHash;
 
 /// Builds a beacon block to be used for testing purposes.
@@ -172,7 +173,10 @@ impl<T: EthSpec> TestingBeaconBlockBuilder<T> {
         num_attestations: usize,
         spec: &ChainSpec,
     ) -> Result<(), BeaconStateError> {
-        let mut slot = self.block.slot - spec.min_attestation_inclusion_delay;
+        let mut slot = self
+            .block
+            .slot
+            .safe_sub(spec.min_attestation_inclusion_delay)?;
         let mut attestations_added = 0;
 
         // Stores the following (in order):
@@ -192,7 +196,7 @@ impl<T: EthSpec> TestingBeaconBlockBuilder<T> {
         // - The slot is too old to be included in a block at this slot.
         // - The `MAX_ATTESTATIONS`.
         loop {
-            if state.slot >= slot + T::slots_per_epoch() {
+            if state.slot >= slot.safe_add(T::slots_per_epoch())? {
                 break;
             }
 
@@ -211,7 +215,7 @@ impl<T: EthSpec> TestingBeaconBlockBuilder<T> {
                 attestations_added += 1;
             }
 
-            slot -= 1;
+            slot.safe_sub_assign(1u64)?;
         }
 
         // Loop through all the committees, splitting each one in half until we have
diff --git a/consensus/types/src/test_utils/builders/testing_beacon_state_builder.rs b/consensus/types/src/test_utils/builders/testing_beacon_state_builder.rs
index 1dda9de98..67a3dae26 100644
--- a/consensus/types/src/test_utils/builders/testing_beacon_state_builder.rs
+++ b/consensus/types/src/test_utils/builders/testing_beacon_state_builder.rs
@@ -143,11 +143,11 @@ impl<T: EthSpec> TestingBeaconStateBuilder<T> {
 
         state.slot = slot;
 
-        state.previous_justified_checkpoint.epoch = epoch - 3;
-        state.current_justified_checkpoint.epoch = epoch - 2;
+        state.previous_justified_checkpoint.epoch = epoch.saturating_sub(3u64);
+        state.current_justified_checkpoint.epoch = epoch.saturating_sub(2u64);
         state.justification_bits = BitVector::from_bytes(vec![0b0000_1111]).unwrap();
 
-        state.finalized_checkpoint.epoch = epoch - 3;
+        state.finalized_checkpoint.epoch = state.previous_justified_checkpoint.epoch;
     }
 
     /// Creates a full set of attestations for the `BeaconState`. Each attestation has full