diff --git a/doc/users/next_whats_new/2018-02-01-AL.rst b/doc/users/next_whats_new/2018-02-01-AL.rst
new file mode 100644
index 000000000000..1acaba83037d
--- /dev/null
+++ b/doc/users/next_whats_new/2018-02-01-AL.rst
@@ -0,0 +1,11 @@
+Added `Axis.get_inverted` and `Axis.set_inverted`
+`````````````````````````````````````````````````
+
+The `Axis.get_inverted` and `Axis.set_inverted` methods query and set whether
+the axis uses "inverted" orientation (i.e. increasing to the left for the
+x-axis and to the bottom for the y-axis).
+
+They perform tasks similar to `Axes.xaxis_inverted`, `Axes.yaxis_inverted`,
+`Axes.invert_xaxis`, and `Axes.invert_yaxis`, with the specific difference that
+`.set_inverted` makes it easier to set the invertedness of an axis regardless
+of whether it had previously been inverted before.
diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 477526b308e4..8287983a3039 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2998,7 +2998,7 @@ def invert_xaxis(self):
         get_xlim, set_xlim
         get_xbound, set_xbound
         """
-        self.set_xlim(self.get_xlim()[::-1], auto=None)
+        self.xaxis.set_inverted(not self.xaxis.get_inverted())
 
     def xaxis_inverted(self):
         """
@@ -3012,8 +3012,7 @@ def xaxis_inverted(self):
         get_xlim, set_xlim
         get_xbound, set_xbound
         """
-        left, right = self.get_xlim()
-        return right < left
+        return self.xaxis.get_inverted()
 
     def get_xbound(self):
         """
@@ -3404,7 +3403,7 @@ def invert_yaxis(self):
         get_ylim, set_ylim
         get_ybound, set_ybound
         """
-        self.set_ylim(self.get_ylim()[::-1], auto=None)
+        self.yaxis.set_inverted(not self.yaxis.get_inverted())
 
     def yaxis_inverted(self):
         """
@@ -3418,8 +3417,7 @@ def yaxis_inverted(self):
         get_ylim, set_ylim
         get_ybound, set_ybound
         """
-        bottom, top = self.get_ylim()
-        return top < bottom
+        return self.yaxis.get_inverted()
 
     def get_ybound(self):
         """
diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index a2eb3e429bd1..0d36c2896bc6 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -909,6 +909,31 @@ def set_data_interval(self):
         '''set the axis data limits'''
         raise NotImplementedError('Derived must override')
 
+    def get_inverted(self):
+        """
+        Return whether the axis is oriented in the "inverse" direction.
+
+        The "normal" direction is increasing to the right for the x-axis and to
+        the top for the y-axis; the "inverse" direction is increasing to the
+        left for the x-axis and to the bottom for the y-axis.
+        """
+        low, high = self.get_view_interval()
+        return high < low
+
+    def set_inverted(self, inverted):
+        """
+        Set whether the axis is oriented in the "inverse" direction.
+
+        The "normal" direction is increasing to the right for the x-axis and to
+        the top for the y-axis; the "inverse" direction is increasing to the
+        left for the x-axis and to the bottom for the y-axis.
+        """
+        a, b = self.get_view_interval()
+        if inverted:
+            self.set_view_interval(max(a, b), min(a, b), ignore=True)
+        else:
+            self.set_view_interval(min(a, b), max(a, b), ignore=True)
+
     def set_default_intervals(self):
         '''set the default limits for the axis data and view interval if they
         are not mutated'''