diff --git a/doc/internals.rst b/doc/internals.rst
index 46c117e312b..b158f12ac6d 100644
--- a/doc/internals.rst
+++ b/doc/internals.rst
@@ -42,6 +42,38 @@ xarray objects via the (readonly) :py:attr:`Dataset.variables
 <xarray.Dataset.variables>` and
 :py:attr:`DataArray.variable <xarray.DataArray.variable>` attributes.
 
+Duck arrays
+-----------
+
+.. warning::
+
+    This is a experimental feature.
+
+xarray can wrap custom `duck array`_ objects as long as they define numpy's
+``shape``, ``dtype`` and ``ndim`` properties and the ``__array__``,
+``__array_ufunc__`` and ``__array_function__`` methods.
+
+In certain situations (e.g. when printing the collapsed preview of
+variables of a ``Dataset``), xarray will display the repr of a `duck array`_
+in a single line, truncating it to a certain number of characters. If that
+would drop too much information, the `duck array`_ may define a
+``_repr_inline_`` method that takes ``max_width`` (number of characters) as an
+argument:
+
+.. code:: python
+
+    class MyDuckArray:
+        ...
+
+        def _repr_inline_(self, max_width):
+            """ format to a single line with at most max_width characters """
+            ...
+
+        ...
+
+.. _duck array: https://numpy.org/neps/nep-0022-ndarray-duck-typing-overview.html
+
+
 Extending xarray
 ----------------
 
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 81ef2cd9e17..573583f0de3 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -29,6 +29,10 @@ New Features
   property for :py:class:`CFTimeIndex` and show ``calendar`` and ``length`` in
   :py:meth:`CFTimeIndex.__repr__` (:issue:`2416`, :pull:`4092`)
   `Aaron Spring <https://github.com/aaronspring>`_.
+- Use a wrapped array's ``_repr_inline_`` method to construct the collapsed ``repr``
+  of :py:class:`DataArray` and :py:class:`Dataset` objects and
+  document the new method in :doc:`internals`. (:pull:`4248`).
+  By `Justus Magin <https://github.com/keewis>`_.
 
 
 Bug fixes
diff --git a/xarray/core/formatting.py b/xarray/core/formatting.py
index 28eaae5f05b..9aa20f2b87e 100644
--- a/xarray/core/formatting.py
+++ b/xarray/core/formatting.py
@@ -261,6 +261,8 @@ def inline_variable_array_repr(var, max_width):
         return inline_dask_repr(var.data)
     elif isinstance(var._data, sparse_array_type):
         return inline_sparse_repr(var.data)
+    elif hasattr(var._data, "_repr_inline_"):
+        return var._data._repr_inline_(max_width)
     elif hasattr(var._data, "__array_function__"):
         return maybe_truncate(repr(var._data).replace("\n", " "), max_width)
     else:
diff --git a/xarray/tests/test_formatting.py b/xarray/tests/test_formatting.py
index 82de8080c80..1cc91266421 100644
--- a/xarray/tests/test_formatting.py
+++ b/xarray/tests/test_formatting.py
@@ -7,6 +7,7 @@
 
 import xarray as xr
 from xarray.core import formatting
+from xarray.core.npcompat import IS_NEP18_ACTIVE
 
 from . import raises_regex
 
@@ -391,6 +392,44 @@ def test_array_repr(self):
         assert actual == expected
 
 
+@pytest.mark.skipif(not IS_NEP18_ACTIVE, reason="requires __array_function__")
+def test_inline_variable_array_repr_custom_repr():
+    class CustomArray:
+        def __init__(self, value, attr):
+            self.value = value
+            self.attr = attr
+
+        def _repr_inline_(self, width):
+            formatted = f"({self.attr}) {self.value}"
+            if len(formatted) > width:
+                formatted = f"({self.attr}) ..."
+
+            return formatted
+
+        def __array_function__(self, *args, **kwargs):
+            return NotImplemented
+
+        @property
+        def shape(self):
+            return self.value.shape
+
+        @property
+        def dtype(self):
+            return self.value.dtype
+
+        @property
+        def ndim(self):
+            return self.value.ndim
+
+    value = CustomArray(np.array([20, 40]), "m")
+    variable = xr.Variable("x", value)
+
+    max_width = 10
+    actual = formatting.inline_variable_array_repr(variable, max_width=10)
+
+    assert actual == value._repr_inline_(max_width)
+
+
 def test_set_numpy_options():
     original_options = np.get_printoptions()
     with formatting.set_numpy_options(threshold=10):