diff --git a/array_api_tests/test_dlpack.py b/array_api_tests/test_dlpack.py
new file mode 100644
index 00000000..3f06a655
--- /dev/null
+++ b/array_api_tests/test_dlpack.py
@@ -0,0 +1,126 @@
+from enum import Enum
+
+from hypothesis import given, strategies as st
+from . import _array_module as xp
+from . import pytest_helpers as ph
+from . import hypothesis_helpers as hh
+
+# dlpack Enum values,
+# https://data-apis.org/array-api/latest/API_specification/generated/array_api.array.__dlpack_device__.html
+
+class DLPackDeviceEnum(Enum):
+    CPU = 1
+    CUDA = 2
+    CPU_PINNED = 3
+    OPENCL = 4
+    VULKAN = 7
+    METAL = 8
+    VPI = 9
+    ROCM = 10
+    CUDA_MANAGED = 13
+    ONE_API = 14
+
+
+def _compatible_devices(devices):
+    """Given a list of devices, filter out dlpack-incompatible ones."""
+    # XXX: there seems to be no better way than try-catch for __dlpack_device__()
+
+    # XXX: this process actually fails with CuPy because CuPy ignores the device= argument
+    # cf https://github.com/data-apis/array-api-compat/issues/337
+    # Luckily, CuPy only supports CUDA devices, and they are all compatible.
+    compatible_ = []
+    for device in devices:
+        x = xp.empty(2, device=device)
+        try:
+            x.__dlpack_device__()
+        except:
+            # case in point: torch.device(type="meta") raises
+            # ValueError: Unknown device type meta for Dlpack
+            pass
+        else:
+            # no exception => device is compatible
+            compatible_.append(device)
+    return compatible_
+
+
+@given(dtype=hh.all_dtypes, data=st.data())
+def test_dlpack_device(dtype, data):
+    """Test the array object __dlpack_device__ method."""
+    # TODO: 1. generate inputs on non-default devices
+    x = xp.empty(3, dtype=dtype)
+    device_type, device_id  = x.__dlpack_device__()
+
+    assert DLPackDeviceEnum(int(device_type))
+    assert isinstance(device_id, int)
+
+
+@given(
+    x=hh.arrays(dtype=hh.all_dtypes, shape=hh.shapes(min_dims=1, max_side=2)),
+    copy_kw=hh.kwargs(
+        copy=st.booleans() | st.none()
+    ),
+    max_version_kw=hh.kwargs(
+        max_version=st.tuples(
+            st.integers(min_value=0, max_value=2),
+            st.integers(min_value=0, max_value=0)
+        )
+    ),
+    dl_device_kw=hh.kwargs(
+        dl_device=st.tuples(  # XXX: the 2023.12 standard only mandates ... kDLCPU ?
+            st.just(DLPackDeviceEnum.CPU.value),
+            st.just(0)
+        )
+    ),
+    data=st.data()
+)
+def test_dunder_dlpack(x, copy_kw, max_version_kw, dl_device_kw, data):
+    repro_snippet = ph.format_snippet(
+        f"x.__dlpack__ with {copy_kw = }, {max_version_kw = } and {dl_device_kw = }"
+    )
+
+    try:
+        x.__dlpack__(**copy_kw, **max_version_kw, **dl_device_kw)
+        # apparently, we cannot do anything with the DLPack capsule from python
+    except Exception as exc:
+        ph.add_note(exc, repro_snippet)
+        raise
+
+
+@given(
+    x=hh.arrays(dtype=hh.all_dtypes, shape=hh.shapes(min_dims=1, max_side=2)),
+    copy_kw=hh.kwargs(copy=st.booleans()),
+    data=st.data()
+)
+def test_from_dlpack(x, copy_kw, data):
+    # TODO: 1. test copy;  2. generate inputs on non-default devices;
+    #       3. test for copy=False cross-device transfers
+    #       4. test 0D arrays / numpy scalars (the latter do not support dlpack ATM)
+
+    copy = copy_kw["copy"] if copy_kw else None
+    if copy is False:
+        # XXX there is no way to tell if a no-copy cross-device transfer is meant to succeed
+        devices = [x.device]
+    else:
+        devices = xp.__array_namespace_info__().devices()
+        devices = _compatible_devices(devices)
+
+    tgt_device_kw = data.draw(
+        hh.kwargs(device=st.sampled_from(devices) | st.none())
+    )
+    tgt_device = tgt_device_kw['device'] if tgt_device_kw else None
+
+    repro_snippet = ph.format_snippet(
+        f"y = from_dlpack({x!r}, **tgt_device_kw, **copy_kw) with {tgt_device_kw=} and {copy_kw=}"
+    )
+    try:
+        y = xp.from_dlpack(x, **tgt_device_kw, **copy_kw)
+
+        if tgt_device is None:
+            assert y.device == x.device
+            assert xp.all(y == x)
+        else:
+            assert y.device == tgt_device
+
+    except Exception as exc:
+        ph.add_note(exc, repro_snippet)
+        raise