diff --git a/doc/interpolation.rst b/doc/interpolation.rst
index 63e9a7cd35e..4cf39807e5a 100644
--- a/doc/interpolation.rst
+++ b/doc/interpolation.rst
@@ -150,8 +150,14 @@ Additional keyword arguments can be passed to scipy's functions.
 
     # fill 0 for the outside of the original coordinates.
     da.interp(x=np.linspace(-0.5, 1.5, 10), kwargs={'fill_value': 0.0})
-    # extrapolation
+    # 1-dimensional extrapolation
     da.interp(x=np.linspace(-0.5, 1.5, 10), kwargs={'fill_value': 'extrapolate'})
+    # multi-dimensional extrapolation
+    da = xr.DataArray(np.sin(0.3 * np.arange(12).reshape(4, 3)),
+                      [('time', np.arange(4)),
+                       ('space', [0.1, 0.2, 0.3])])
+
+    da.interp(time=4, space=np.linspace(-0.1, 0.5, 10), kwargs={'fill_value': None})
 
 
 Advanced Interpolation
diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 1d00cb369d1..cab886885e8 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -86,6 +86,10 @@ Documentation
   (:pull:`3935`). By `Spencer Clark <https://github.com/spencerkclark>`_.
 - Updated the list of current core developers. (:issue:`3892`)
   By `Tom Nicholas <https://github.com/TomNicholas>`_.
+- Add example for multi-dimensional extrapolation and note different behavior
+  of ``kwargs`` in :py:meth:`Dataset.interp` and :py:meth:`DataArray.interp`
+  for 1-d and n-d interpolation (:pull:`3956`).
+  By `Matthias Riße <https://github.com/risebell>`_.
 
 Internal Changes
 ~~~~~~~~~~~~~~~~
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index 63cba53b689..a17fab383a6 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -1366,7 +1366,9 @@ def interp(
             first. If True, x has to be an array of monotonically increasing
             values.
         kwargs: dictionary
-            Additional keyword passed to scipy's interpolator.
+            Additional keyword arguments passed to scipy's interpolator. Valid
+            options and their behavior depend on if 1-dimensional or
+            multi-dimensional interpolation is used.
         ``**coords_kwargs`` : {dim: coordinate, ...}, optional
             The keyword arguments form of ``coords``.
             One of coords or coords_kwargs must be provided.
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index dd1e31cc61a..d811d54847f 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2570,7 +2570,9 @@ def interp(
             coordinates are assumed to be an array of monotonically increasing
             values.
         kwargs: dictionary, optional
-            Additional keyword passed to scipy's interpolator.
+            Additional keyword arguments passed to scipy's interpolator. Valid
+            options and their behavior depend on if 1-dimensional or
+            multi-dimensional interpolation is used.
         **coords_kwargs : {dim: coordinate, ...}, optional
             The keyword arguments form of ``coords``.
             One of coords or coords_kwargs must be provided.