diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index ff67ea20073..355e19ee2a8 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -38,6 +38,8 @@ New Features
   By `Thomas Hirtz <https://github.com/thomashirtz>`_.
 - allow passing a function to ``combine_attrs`` (:pull:`4896`).
   By `Justus Magin <https://github.com/keewis>`_.
+- Allow plotting categorical data (:pull:`5464`).
+  By `Jimmy Westling <https://github.com/illviljan>`_.
 
 Breaking changes
 ~~~~~~~~~~~~~~~~
diff --git a/xarray/plot/plot.py b/xarray/plot/plot.py
index f530427562a..10ebcc07664 100644
--- a/xarray/plot/plot.py
+++ b/xarray/plot/plot.py
@@ -925,18 +925,26 @@ def imshow(x, y, z, ax, **kwargs):
             "imshow requires 1D coordinates, try using pcolormesh or contour(f)"
         )
 
-    # Centering the pixels- Assumes uniform spacing
-    try:
-        xstep = (x[1] - x[0]) / 2.0
-    except IndexError:
-        # Arbitrary default value, similar to matplotlib behaviour
-        xstep = 0.1
-    try:
-        ystep = (y[1] - y[0]) / 2.0
-    except IndexError:
-        ystep = 0.1
-    left, right = x[0] - xstep, x[-1] + xstep
-    bottom, top = y[-1] + ystep, y[0] - ystep
+    def _center_pixels(x):
+        """Center the pixels on the coordinates."""
+        if np.issubdtype(x.dtype, str):
+            # When using strings as inputs imshow converts it to
+            # integers. Choose extent values which puts the indices in
+            # in the center of the pixels:
+            return 0 - 0.5, len(x) - 0.5
+
+        try:
+            # Center the pixels assuming uniform spacing:
+            xstep = 0.5 * (x[1] - x[0])
+        except IndexError:
+            # Arbitrary default value, similar to matplotlib behaviour:
+            xstep = 0.1
+
+        return x[0] - xstep, x[-1] + xstep
+
+    # Center the pixels:
+    left, right = _center_pixels(x)
+    top, bottom = _center_pixels(y)
 
     defaults = {"origin": "upper", "interpolation": "nearest"}
 
@@ -967,6 +975,13 @@ def imshow(x, y, z, ax, **kwargs):
 
     primitive = ax.imshow(z, **defaults)
 
+    # If x or y are strings the ticklabels have been replaced with
+    # integer indices. Replace them back to strings:
+    for axis, v in [("x", x), ("y", y)]:
+        if np.issubdtype(v.dtype, str):
+            getattr(ax, f"set_{axis}ticks")(np.arange(len(v)))
+            getattr(ax, f"set_{axis}ticklabels")(v)
+
     return primitive
 
 
@@ -1011,9 +1026,13 @@ def pcolormesh(x, y, z, ax, infer_intervals=None, **kwargs):
         else:
             infer_intervals = True
 
-    if infer_intervals and (
-        (np.shape(x)[0] == np.shape(z)[1])
-        or ((x.ndim > 1) and (np.shape(x)[1] == np.shape(z)[1]))
+    if (
+        infer_intervals
+        and not np.issubdtype(x.dtype, str)
+        and (
+            (np.shape(x)[0] == np.shape(z)[1])
+            or ((x.ndim > 1) and (np.shape(x)[1] == np.shape(z)[1]))
+        )
     ):
         if len(x.shape) == 1:
             x = _infer_interval_breaks(x, check_monotonic=True)
@@ -1022,7 +1041,11 @@ def pcolormesh(x, y, z, ax, infer_intervals=None, **kwargs):
             x = _infer_interval_breaks(x, axis=1)
             x = _infer_interval_breaks(x, axis=0)
 
-    if infer_intervals and (np.shape(y)[0] == np.shape(z)[0]):
+    if (
+        infer_intervals
+        and not np.issubdtype(y.dtype, str)
+        and (np.shape(y)[0] == np.shape(z)[0])
+    ):
         if len(y.shape) == 1:
             y = _infer_interval_breaks(y, check_monotonic=True)
         else:
diff --git a/xarray/plot/utils.py b/xarray/plot/utils.py
index 416d56aa620..db85a5908c0 100644
--- a/xarray/plot/utils.py
+++ b/xarray/plot/utils.py
@@ -604,7 +604,14 @@ def _ensure_plottable(*args):
     Raise exception if there is anything in args that can't be plotted on an
     axis by matplotlib.
     """
-    numpy_types = [np.floating, np.integer, np.timedelta64, np.datetime64, np.bool_]
+    numpy_types = [
+        np.floating,
+        np.integer,
+        np.timedelta64,
+        np.datetime64,
+        np.bool_,
+        np.str_,
+    ]
     other_types = [datetime]
     try:
         import cftime
diff --git a/xarray/tests/test_plot.py b/xarray/tests/test_plot.py
index bbd7c31fa16..e833654138a 100644
--- a/xarray/tests/test_plot.py
+++ b/xarray/tests/test_plot.py
@@ -684,10 +684,9 @@ def test_format_string(self):
     def test_can_pass_in_axis(self):
         self.pass_in_axis(self.darray.plot.line)
 
-    def test_nonnumeric_index_raises_typeerror(self):
+    def test_nonnumeric_index(self):
         a = DataArray([1, 2, 3], {"letter": ["a", "b", "c"]}, dims="letter")
-        with pytest.raises(TypeError, match=r"[Pp]lot"):
-            a.plot.line()
+        a.plot.line()
 
     def test_primitive_returned(self):
         p = self.darray.plot.line()
@@ -1162,9 +1161,13 @@ def test_3d_raises_valueerror(self):
         with pytest.raises(ValueError, match=r"DataArray must be 2d"):
             self.plotfunc(a)
 
-    def test_nonnumeric_index_raises_typeerror(self):
+    def test_nonnumeric_index(self):
         a = DataArray(easy_array((3, 2)), coords=[["a", "b", "c"], ["d", "e"]])
-        with pytest.raises(TypeError, match=r"[Pp]lot"):
+        if self.plotfunc.__name__ == "surface":
+            # ax.plot_surface errors with nonnumerics:
+            with pytest.raises(Exception):
+                self.plotfunc(a)
+        else:
             self.plotfunc(a)
 
     def test_multiindex_raises_typeerror(self):