diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 71edc6281d6a..8ac56ab9bdb6 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -477,7 +477,6 @@ def __init__(self, fig, rect,
         if self._position.width < 0 or self._position.height < 0:
             raise ValueError('Width and height specified must be non-negative')
         self._originalPosition = self._position.frozen()
-        # self.set_axes(self)
         self.axes = self
         self._aspect = 'auto'
         self._adjustable = 'box'
@@ -501,7 +500,7 @@ def __init__(self, fig, rect,
             facecolor = rcParams['axes.facecolor']
         self._facecolor = facecolor
         self._frameon = frameon
-        self._axisbelow = rcParams['axes.axisbelow']
+        self.set_axisbelow(rcParams['axes.axisbelow'])
 
         self._rasterization_zorder = None
         self._connected = {}  # a dict from events to (id, func)
@@ -2537,18 +2536,7 @@ def draw(self, renderer=None, inframe=False):
 
         self._update_title_position(renderer)
 
-        if self.axison and not inframe:
-            if self._axisbelow is True:
-                self.xaxis.set_zorder(0.5)
-                self.yaxis.set_zorder(0.5)
-            elif self._axisbelow is False:
-                self.xaxis.set_zorder(2.5)
-                self.yaxis.set_zorder(2.5)
-            else:
-                # 'line': above patches, below lines
-                self.xaxis.set_zorder(1.5)
-                self.yaxis.set_zorder(1.5)
-        else:
+        if not self.axison or inframe:
             for _axis in self._get_axis_list():
                 artists.remove(_axis)
 
@@ -2620,9 +2608,7 @@ def get_renderer_cache(self):
     # Axes rectangle characteristics
 
     def get_frame_on(self):
-        """
-        Get whether the axes rectangle patch is drawn.
-        """
+        """Get whether the axes rectangle patch is drawn."""
         return self._frameon
 
     def set_frame_on(self, b):
@@ -2644,13 +2630,26 @@ def get_axisbelow(self):
 
     def set_axisbelow(self, b):
         """
-        Set whether axis ticks and gridlines are above or below most artists.
+        Set the zorder for the axes ticks and gridlines.
 
         Parameters
         ----------
         b : bool or 'line'
+            ``True`` corresponds to a zorder of 0.5, ``False`` to a zorder of
+            2.5, and ``"line"`` to a zorder of 1.5.
+
         """
-        self._axisbelow = validate_axisbelow(b)
+        self._axisbelow = axisbelow = validate_axisbelow(b)
+        if axisbelow is True:
+            zorder = 0.5
+        elif axisbelow is False:
+            zorder = 2.5
+        elif axisbelow == "line":
+            zorder = 1.5
+        else:
+            raise ValueError("Unexpected axisbelow value")
+        for axis in self._get_axis_list():
+            axis.set_zorder(zorder)
         self.stale = True
 
     @docstring.dedent_interpd
@@ -2678,6 +2677,8 @@ def grid(self, b=None, which='major', axis='both', **kwargs):
 
         %(Line2D)s
 
+        Note that the grid will be drawn according to the axes' zorder and not
+        its own.
         """
         if len(kwargs):
             b = True
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index 82c44ffad0ca..85d5761cc7de 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -786,7 +786,6 @@ def test_imshow_masked_interpolation():
     N = 20
     n = colors.Normalize(vmin=0, vmax=N*N-1)
 
-    # data = np.random.random((N, N))*N*N
     data = np.arange(N*N, dtype='float').reshape(N, N)
 
     data[5, 5] = -1
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 16bb0ebec65e..d9e24280535c 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -272,28 +272,28 @@ def draw(self, renderer):
         renderer.eye = self.eye
         renderer.get_axis_position = self.get_axis_position
 
-        # Calculate projection of collections and zorder them
+        # Calculate projection of collections and patches and zorder them.
+        # Make sure they are drawn above the grids.
+        zorder_offset = max(axis.get_zorder()
+                            for axis in self._get_axis_list()) + 1
         for i, col in enumerate(
                 sorted(self.collections,
                        key=lambda col: col.do_3d_projection(renderer),
                        reverse=True)):
-            col.zorder = i
-
-        # Calculate projection of patches and zorder them
+            col.zorder = zorder_offset + i
         for i, patch in enumerate(
                 sorted(self.patches,
                        key=lambda patch: patch.do_3d_projection(renderer),
                        reverse=True)):
-            patch.zorder = i
+            patch.zorder = zorder_offset + i
 
         if self._axis3don:
-            axes = (self.xaxis, self.yaxis, self.zaxis)
             # Draw panes first
-            for ax in axes:
-                ax.draw_pane(renderer)
+            for axis in self._get_axis_list():
+                axis.draw_pane(renderer)
             # Then axes
-            for ax in axes:
-                ax.draw(renderer)
+            for axis in self._get_axis_list():
+                axis.draw(renderer)
 
         # Then rest
         super().draw(renderer)
@@ -1283,33 +1283,6 @@ def set_frame_on(self, b):
         self._frameon = bool(b)
         self.stale = True
 
-    def get_axisbelow(self):
-        """
-        Get whether axis below is true or not.
-
-        For axes3d objects, this will always be *True*
-
-        .. versionadded :: 1.1.0
-            This function was added for completeness.
-        """
-        return True
-
-    def set_axisbelow(self, b):
-        """
-        Set whether axis ticks and gridlines are above or below most artists.
-
-        For axes3d objects, this will ignore any settings and just use *True*
-
-        .. versionadded :: 1.1.0
-            This function was added for completeness.
-
-        Parameters
-        ----------
-        b : bool
-        """
-        self._axisbelow = True
-        self.stale = True
-
     def grid(self, b=True, **kwargs):
         '''
         Set / unset 3D grid.