diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index f36591741..0f517fac9 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -88,6 +88,17 @@ jobs:
         run: sudo apt-get install libopenblas-dev gfortran
       - run: ./scripts/all-tests.sh "$FEATURES" ${{ matrix.rust }}
 
+  miri:
+    runs-on: ubuntu-latest
+    name: miri
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@nightly
+        with:
+          components: miri
+      - uses: Swatinem/rust-cache@v2
+      - run: ./scripts/miri-tests.sh
+
   cross_test:
     #if: ${{ github.event_name == 'merge_group' }}
     runs-on: ubuntu-latest
@@ -149,6 +160,7 @@ jobs:
       - format  # should format be required?
       - nostd
       - tests
+      - miri
       - cross_test
       - cargo-careful
       - docs
diff --git a/ndarray-rand/tests/tests.rs b/ndarray-rand/tests/tests.rs
index 2db040310..e39347c0c 100644
--- a/ndarray-rand/tests/tests.rs
+++ b/ndarray-rand/tests/tests.rs
@@ -57,6 +57,7 @@ fn oversampling_without_replacement_should_panic()
 }
 
 quickcheck! {
+    #[cfg_attr(miri, ignore)] // Takes an insufferably long time
     fn oversampling_with_replacement_is_fine(m: u8, n: u8) -> TestResult {
         let (m, n) = (m as usize, n as usize);
         let a = Array::random((m, n), Uniform::new(0., 2.));
@@ -86,6 +87,7 @@ quickcheck! {
 
 #[cfg(feature = "quickcheck")]
 quickcheck! {
+    #[cfg_attr(miri, ignore)] // This takes *forever* with Miri
     fn sampling_behaves_as_expected(m: u8, n: u8, strategy: SamplingStrategy) -> TestResult {
         let (m, n) = (m as usize, n as usize);
         let a = Array::random((m, n), Uniform::new(0., 2.));
diff --git a/scripts/miri-tests.sh b/scripts/miri-tests.sh
new file mode 100755
index 000000000..0100f3e6a
--- /dev/null
+++ b/scripts/miri-tests.sh
@@ -0,0 +1,18 @@
+#!/bin/sh
+
+set -x
+set -e
+
+# We rely on layout-dependent casts, which should be covered with #[repr(transparent)]
+# This should catch if we missed that
+RUSTFLAGS="-Zrandomize-layout"
+
+# Miri reports a stacked borrow violation deep within rayon, in a crate called crossbeam-epoch
+# The crate has a PR to fix this: https://github.com/crossbeam-rs/crossbeam/pull/871
+# but using Miri's tree borrow mode may resolve it for now.
+# Disabled until we can figure out a different rayon issue: https://github.com/rust-lang/miri/issues/1371
+# MIRIFLAGS="-Zmiri-tree-borrows"
+
+# General tests
+# Note that we exclude blas feature because Miri can't do cblas_gemm
+cargo miri test -v -p ndarray -p ndarray-rand --features approx,serde
diff --git a/src/dimension/mod.rs b/src/dimension/mod.rs
index 601f0dc43..eb07252b2 100644
--- a/src/dimension/mod.rs
+++ b/src/dimension/mod.rs
@@ -1020,6 +1020,7 @@ mod test
     }
 
     quickcheck! {
+        #[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
         // FIXME: This test is extremely slow, even with i16 values, investigate
         fn arith_seq_intersect_correct(
             first1: i8, len1: i8, step1: i8,
diff --git a/tests/array.rs b/tests/array.rs
index 696904dab..ac38fdd03 100644
--- a/tests/array.rs
+++ b/tests/array.rs
@@ -2629,6 +2629,7 @@ mod array_cow_tests
         });
     }
 
+    #[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
     #[test]
     fn test_clone_from()
     {
diff --git a/tests/azip.rs b/tests/azip.rs
index d1ab5ba2a..96be9d913 100644
--- a/tests/azip.rs
+++ b/tests/azip.rs
@@ -216,7 +216,7 @@ fn test_azip2_sum()
 }
 
 #[test]
-#[cfg(feature = "approx")]
+#[cfg(all(feature = "approx", feature = "std"))]
 fn test_azip3_slices()
 {
     use approx::assert_abs_diff_eq;
diff --git a/tests/dimension.rs b/tests/dimension.rs
index 6a9207e4c..fe53d96b3 100644
--- a/tests/dimension.rs
+++ b/tests/dimension.rs
@@ -323,6 +323,7 @@ fn test_array_view()
 }
 
 #[test]
+#[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
 #[cfg(feature = "std")]
 #[allow(clippy::cognitive_complexity)]
 fn test_all_ndindex()
diff --git a/tests/iterators.rs b/tests/iterators.rs
index 908b64d15..bdfd3ee50 100644
--- a/tests/iterators.rs
+++ b/tests/iterators.rs
@@ -971,6 +971,7 @@ fn test_into_iter_2d()
     assert_eq!(v, [1, 3, 2, 4]);
 }
 
+#[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
 #[test]
 fn test_into_iter_sliced()
 {
diff --git a/tests/oper.rs b/tests/oper.rs
index 5e3e669d0..401913e2b 100644
--- a/tests/oper.rs
+++ b/tests/oper.rs
@@ -502,6 +502,7 @@ fn scaled_add()
 }
 
 #[cfg(feature = "approx")]
+#[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
 #[test]
 fn scaled_add_2()
 {
@@ -540,6 +541,7 @@ fn scaled_add_2()
 }
 
 #[cfg(feature = "approx")]
+#[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
 #[test]
 fn scaled_add_3()
 {
@@ -592,6 +594,7 @@ fn scaled_add_3()
 }
 
 #[cfg(feature = "approx")]
+#[cfg_attr(miri, ignore)]
 #[test]
 fn gen_mat_mul()
 {
@@ -681,6 +684,7 @@ fn gen_mat_mul_i32()
 
 #[cfg(feature = "approx")]
 #[test]
+#[cfg_attr(miri, ignore)] // Takes too long
 fn gen_mat_vec_mul()
 {
     use approx::assert_relative_eq;
@@ -746,6 +750,7 @@ fn gen_mat_vec_mul()
 }
 
 #[cfg(feature = "approx")]
+#[cfg_attr(miri, ignore)] // Very slow on CI/CD machines
 #[test]
 fn vec_mat_mul()
 {