diff --git a/.github/workflows/ci-build.yaml b/.github/workflows/ci-build.yaml
index 833604b9c537..a1046880cd60 100644
--- a/.github/workflows/ci-build.yaml
+++ b/.github/workflows/ci-build.yaml
@@ -60,7 +60,10 @@ jobs:
             os: ubuntu-latest
             enable-x64: 1
             enable-omnistaging: 0
-            package-overrides: "none"
+            # Test experimental NumPy dispatch
+            # TODO(shoyer): remove cython after
+            # https://github.com/seberg/numpy-dispatch/pull/5 is merged
+            package-overrides: "cython git+https://github.com/seberg/numpy-dispatch.git"
             num_generated_cases: 25
           - python-version: 3.6
             os: ubuntu-latest
diff --git a/jax/core.py b/jax/core.py
index 8a5576b916cb..1ff93a45a932 100644
--- a/jax/core.py
+++ b/jax/core.py
@@ -469,6 +469,9 @@ def __len__(self):
   def aval(self):
     raise NotImplementedError("must override")
 
+  # Python looks up special methods only on classes, not instances. This means
+  # these methods needs to be defined explicitly rather than relying on
+  # __getattr__ (short of using a metaclass).
   def __neg__(self): return self.aval._neg(self)
   def __pos__(self): return self.aval._pos(self)
   def __eq__(self, other): return self.aval._eq(self, other)
@@ -528,6 +531,9 @@ def __complex__(self):
   def __setitem__(self, idx, val):
     raise TypeError("JAX 'Tracer' objects do not support item assignment")
 
+  # NumPy also only looks up special methods on classes.
+  def __array_module__(self, types): return self.aval._array_module(self, types)
+
   def __getattr__(self, name):
     # if the aval property raises an AttributeError, gets caught here
     assert skip_checks or name != "aval"
diff --git a/jax/numpy/lax_numpy.py b/jax/numpy/lax_numpy.py
index 6610a3ece318..c3c43a1131ad 100644
--- a/jax/numpy/lax_numpy.py
+++ b/jax/numpy/lax_numpy.py
@@ -36,6 +36,7 @@
 import numpy as np
 import opt_einsum
 
+import jax
 from jax import jit, custom_jvp
 from .vectorize import vectorize
 from ._util import _wraps
@@ -4574,6 +4575,21 @@ def _operator_round(number, ndigits=None):
 setattr(DeviceArray, "nbytes", property(_nbytes))
 
 
+# Experimental support for NumPy's module dispatch with NEP-37.
+# Currently requires https://github.com/seberg/numpy-dispatch
+_JAX_ARRAY_TYPES = (UnshapedArray, DeviceArray, core.Tracer)
+_HANDLED_ARRAY_TYPES = _JAX_ARRAY_TYPES + (np.ndarray,)
+
+def __array_module__(self, types):
+  if builtins.all(issubclass(t, _HANDLED_ARRAY_TYPES) for t in types):
+    return jax.numpy
+  else:
+    return NotImplemented
+
+setattr(ShapedArray, "_array_module", staticmethod(__array_module__))
+setattr(DeviceArray, "__array_module__", __array_module__)
+
+
 # Extra methods that are handy
 setattr(ShapedArray, "broadcast", core.aval_method(lax.broadcast))
 setattr(ShapedArray, "broadcast_in_dim", core.aval_method(lax.broadcast_in_dim))
diff --git a/tests/lax_numpy_test.py b/tests/lax_numpy_test.py
index 3a93e52284a9..2684b5454ce1 100644
--- a/tests/lax_numpy_test.py
+++ b/tests/lax_numpy_test.py
@@ -28,6 +28,10 @@
 from absl.testing import parameterized
 
 import numpy as np
+try:
+  import numpy_dispatch
+except ImportError:
+  numpy_dispatch = None
 
 import jax
 import jax.ops
@@ -585,6 +589,27 @@ def testBinaryOperatorDefers(self, op_name, rng_factory, dtype):
       with self.assertRaises(TypeError):
         op(arg, other)
 
+  def testArrayModule(self):
+    if numpy_dispatch is None:
+      raise SkipTest('requires https://github.com/seberg/numpy-dispatch')
+
+    jnp_array = jnp.array(1.0)
+    np_array = np.array(1.0)
+
+    with numpy_dispatch.ensure_dispatching():
+      module = numpy_dispatch.get_array_module(jnp_array)
+      self.assertIs(module, jnp)
+
+      module = numpy_dispatch.get_array_module(jnp_array, np_array)
+      self.assertIs(module, jnp)
+
+      def f(x):
+        module = numpy_dispatch.get_array_module(x)
+        self.assertIs(module, jnp)
+        return x
+      jax.jit(f)(jnp_array)
+      jax.grad(f)(jnp_array)
+
   @parameterized.named_parameters(itertools.chain.from_iterable(
       jtu.cases_from_list(
         {"testcase_name": jtu.format_test_name_suffix(