diff --git a/doc/api/next_api_changes/2019-02-28-AL.rst b/doc/api/next_api_changes/2019-02-28-AL.rst
new file mode 100644
index 000000000000..1e7a99627f46
--- /dev/null
+++ b/doc/api/next_api_changes/2019-02-28-AL.rst
@@ -0,0 +1,26 @@
+``Axes.label_outer``, ``Axes.is_last_row``, and ``Axes.is_last_col`` now work correctly for axes spanning multiple rows or columns
+``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
+
+``Axes.label_outer`` now correctly keep the x labels and tick labels visible
+for Axes spanning multiple rows, as long as they cover the last row of the Axes
+grid.  (This is consistent with keeping the y labels and tick labels visible
+for Axes spanning multiple columns as long as they cover the first column of
+the Axes grid.)
+
+The ``Axes.is_last_row`` and ``Axes.is_last_col`` methods now correctly return
+True for Axes spanning multiple rows, as long as they cover the last row or
+column respectively.  Again this is consistent with the behavior for axes
+covering the first row or column.
+
+The ``Axes.rowNum`` and ``Axes.colNum`` attributes are deprecated, as they only
+refer to the first grid cell covered by the Axes.  Instead, use the new
+``ax.get_subplotspec().rowspan`` and ``ax.get_subplotspec().colspan``
+properties, which are `range` objects indicating the whole span of rows and
+columns covered by the subplot.
+
+(Note that all methods and attributes mentioned here actually only exist on
+the ``Subplot`` subclass of `Axes`, which is used for grid-positioned Axes but
+not for Axes positioned directly in absolute coordinates.)
+
+The `.GridSpec` class gained the ``nrows`` and ``ncols`` properties as more
+explicit synonyms for the parameters returned by ``GridSpec.get_geometry``.
diff --git a/lib/matplotlib/axes/_subplots.py b/lib/matplotlib/axes/_subplots.py
index 6ba9439f6b86..e216de13426c 100644
--- a/lib/matplotlib/axes/_subplots.py
+++ b/lib/matplotlib/axes/_subplots.py
@@ -1,7 +1,7 @@
 import functools
 import uuid
 
-from matplotlib import docstring
+from matplotlib import cbook, docstring
 import matplotlib.artist as martist
 from matplotlib.axes._axes import Axes
 from matplotlib.gridspec import GridSpec, SubplotSpec
@@ -125,26 +125,33 @@ def get_gridspec(self):
 
     def update_params(self):
         """update the subplot position from fig.subplotpars"""
-
-        self.figbox, self.rowNum, self.colNum, self.numRows, self.numCols = \
+        self.figbox, _, _, self.numRows, self.numCols = \
             self.get_subplotspec().get_position(self.figure,
                                                 return_all=True)
 
-    def is_first_col(self):
-        return self.colNum == 0
+    @cbook.deprecated("3.2", alternative="ax.get_subplotspec().rowspan.start")
+    def rowNum(self):
+        return self.get_subplotspec().rowspan.start
+
+    @cbook.deprecated("3.2", alternative="ax.get_subplotspec().colspan.start")
+    def colNum(self):
+        return self.get_subplotspec().colspan.start
 
     def is_first_row(self):
-        return self.rowNum == 0
+        return self.get_subplotspec().rowspan.start == 0
 
     def is_last_row(self):
-        return self.rowNum == self.numRows - 1
+        return self.get_subplotspec().rowspan.stop == self.get_gridspec().nrows
+
+    def is_first_col(self):
+        return self.get_subplotspec().colspan.start == 0
 
     def is_last_col(self):
-        return self.colNum == self.numCols - 1
+        return self.get_subplotspec().colspan.stop == self.get_gridspec().ncols
 
-    # COVERAGE NOTE: Never used internally.
     def label_outer(self):
-        """Only show "outer" labels and tick labels.
+        """
+        Only show "outer" labels and tick labels.
 
         x-labels are only kept for subplots on the last row; y-labels only for
         subplots on the first column.
diff --git a/lib/matplotlib/gridspec.py b/lib/matplotlib/gridspec.py
index 14f21930219e..18cd55920ba8 100644
--- a/lib/matplotlib/gridspec.py
+++ b/lib/matplotlib/gridspec.py
@@ -59,6 +59,11 @@ def __repr__(self):
             optionals=height_arg + width_arg,
             )
 
+    nrows = property(lambda self: self._nrows,
+                     doc="The number of rows in the grid.")
+    ncols = property(lambda self: self._ncols,
+                     doc="The number of columns in the grid.")
+
     def get_geometry(self):
         """
         Return a tuple containing the number of rows and columns in the grid.
@@ -566,6 +571,18 @@ def get_rows_columns(self):
         row_stop, col_stop = divmod(self.num2, ncols)
         return nrows, ncols, row_start, row_stop, col_start, col_stop
 
+    @property
+    def rowspan(self):
+        """The rows spanned by this subplot, as a `range` object."""
+        ncols = self.get_gridspec().ncols
+        return range(self.num1 // ncols, self.num2 // ncols + 1)
+
+    @property
+    def colspan(self):
+        """The columns spanned by this subplot, as a `range` object."""
+        ncols = self.get_gridspec().ncols
+        return range(self.num1 % ncols, self.num2 % ncols + 1)
+
     def get_position(self, figure, return_all=False):
         """
         Update the subplot position from ``figure.subplotpars``.
diff --git a/lib/matplotlib/tests/test_subplots.py b/lib/matplotlib/tests/test_subplots.py
index c581ec81086c..782d56d736ae 100644
--- a/lib/matplotlib/tests/test_subplots.py
+++ b/lib/matplotlib/tests/test_subplots.py
@@ -26,16 +26,13 @@ def check_shared(axs, x_shared, y_shared):
 
 
 def check_visible(axs, x_visible, y_visible):
-    def tostr(v):
-        return "invisible" if v else "visible"
-
-    for ax, vx, vy in zip(axs, x_visible, y_visible):
+    for i, (ax, vx, vy) in enumerate(zip(axs, x_visible, y_visible)):
         for l in ax.get_xticklabels() + [ax.get_xaxis().offsetText]:
             assert l.get_visible() == vx, \
-                    "X axis was incorrectly %s" % (tostr(vx))
+                    f"Visibility of x axis #{i} is incorrectly {vx}"
         for l in ax.get_yticklabels() + [ax.get_yaxis().offsetText]:
             assert l.get_visible() == vy, \
-                    "Y axis was incorrectly %s" % (tostr(vy))
+                    f"Visibility of y axis #{i} is incorrectly {vy}"
 
 
 def test_shared():
@@ -99,6 +96,26 @@ def test_shared():
     check_visible(axs, [False, False, True, True], [True, False, True, False])
 
 
+def test_label_outer_span():
+    fig = plt.figure()
+    gs = fig.add_gridspec(3, 3)
+    # +---+---+---+
+    # |   1   |   |
+    # +---+---+---+
+    # |   |   | 3 |
+    # + 2 +---+---+
+    # |   | 4 |   |
+    # +---+---+---+
+    a1 = fig.add_subplot(gs[0, 0:2])
+    a2 = fig.add_subplot(gs[1:3, 0])
+    a3 = fig.add_subplot(gs[1, 2])
+    a4 = fig.add_subplot(gs[2, 1])
+    for ax in fig.axes:
+        ax.label_outer()
+    check_visible(
+        fig.axes, [False, True, False, True], [True, True, False, False])
+
+
 def test_shared_and_moved():
     # test if sharey is on, but then tick_left is called that labels don't
     # re-appear.  Seaborn does this just to be sure yaxis is on left...