diff --git a/doc/users/next_whats_new/inset_axes_improvements.rst b/doc/users/next_whats_new/inset_axes_improvements.rst
new file mode 100644
index 000000000000..8ff7d82cfb28
--- /dev/null
+++ b/doc/users/next_whats_new/inset_axes_improvements.rst
@@ -0,0 +1,6 @@
+Axes.inset_axes Flexibility
+---------------------------
+
+`matplotlib.axes.Axes.inset_axes` now accepts the *projection*, *polar* and
+*axes_class* keyword arguments, so that subclasses of `matplotlib.axes.Axes` may
+be returned.
\ No newline at end of file
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 3026e681f742..5399b14374ce 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -326,13 +326,27 @@ def inset_axes(self, bounds, *, transform=None, zorder=5, **kwargs):
             Defaults to `ax.transAxes`, i.e. the units of *rect* are in
             Axes-relative coordinates.
 
+        projection : {None, 'aitoff', 'hammer', 'lambert', 'mollweide', \
+'polar', 'rectilinear', str}, optional
+            The projection type of the inset `~.axes.Axes`. *str* is the name
+            of a custom projection, see `~matplotlib.projections`. The default
+            None results in a 'rectilinear' projection.
+
+        polar : bool, default: False
+            If True, equivalent to projection='polar'.
+
+        axes_class : subclass type of `~.axes.Axes`, optional
+            The `.axes.Axes` subclass that is instantiated.  This parameter
+            is incompatible with *projection* and *polar*.  See
+            :ref:`axisartist_users-guide-index` for examples.
+
         zorder : number
             Defaults to 5 (same as `.Axes.legend`).  Adjust higher or lower
             to change whether it is above or below data plotted on the
             parent Axes.
 
         **kwargs
-            Other keyword arguments are passed on to the child `.Axes`.
+            Other keyword arguments are passed on to the inset Axes class.
 
         Returns
         -------
@@ -358,7 +372,10 @@ def inset_axes(self, bounds, *, transform=None, zorder=5, **kwargs):
         # This puts the rectangle into figure-relative coordinates.
         inset_locator = _TransformedBoundsLocator(bounds, transform)
         bounds = inset_locator(self, None).bounds
-        inset_ax = Axes(self.figure, bounds, zorder=zorder, **kwargs)
+        projection_class, pkw = self.figure._process_projection_requirements(
+                bounds, **kwargs)
+        inset_ax = projection_class(self.figure, bounds, zorder=zorder, **pkw)
+
         # this locator lets the axes move if in data coordinates.
         # it gets called in `ax.apply_aspect() (of all places)
         inset_ax.set_axes_locator(inset_locator)
diff --git a/lib/matplotlib/tests/baseline_images/test_axes/inset_polar.png b/lib/matplotlib/tests/baseline_images/test_axes/inset_polar.png
new file mode 100644
index 000000000000..b7b7faf198ec
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_axes/inset_polar.png differ
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index b2bc70ff6143..358b911c45fa 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -26,10 +26,13 @@
 import matplotlib.markers as mmarkers
 import matplotlib.patches as mpatches
 import matplotlib.path as mpath
+from matplotlib.projections.geo import HammerAxes
+from matplotlib.projections.polar import PolarAxes
 import matplotlib.pyplot as plt
 import matplotlib.text as mtext
 import matplotlib.ticker as mticker
 import matplotlib.transforms as mtransforms
+import mpl_toolkits.axisartist as AA
 from numpy.testing import (
     assert_allclose, assert_array_equal, assert_array_almost_equal)
 from matplotlib.testing.decorators import (
@@ -2543,8 +2546,6 @@ def get_next_color():
 
 def test_as_mpl_axes_api():
     # tests the _as_mpl_axes api
-    from matplotlib.projections.polar import PolarAxes
-
     class Polar:
         def __init__(self):
             self.theta_offset = 0
@@ -6614,6 +6615,31 @@ def test_zoom_inset():
         axin1.get_position().get_points(), xx, rtol=1e-4)
 
 
+@image_comparison(['inset_polar.png'], remove_text=True, style='mpl20')
+def test_inset_polar():
+    _, ax = plt.subplots()
+    axins = ax.inset_axes([0.5, 0.1, 0.45, 0.45], polar=True)
+    assert isinstance(axins, PolarAxes)
+
+    r = np.arange(0, 2, 0.01)
+    theta = 2 * np.pi * r
+
+    ax.plot(theta, r)
+    axins.plot(theta, r)
+
+
+def test_inset_projection():
+    _, ax = plt.subplots()
+    axins = ax.inset_axes([0.2, 0.2, 0.3, 0.3], projection="hammer")
+    assert isinstance(axins, HammerAxes)
+
+
+def test_inset_subclass():
+    _, ax = plt.subplots()
+    axins = ax.inset_axes([0.2, 0.2, 0.3, 0.3], axes_class=AA.Axes)
+    assert isinstance(axins, AA.Axes)
+
+
 @pytest.mark.parametrize('x_inverted', [False, True])
 @pytest.mark.parametrize('y_inverted', [False, True])
 def test_indicate_inset_inverted(x_inverted, y_inverted):