diff --git a/doc/api/next_api_changes/deprecations.rst b/doc/api/next_api_changes/deprecations.rst
index 83338d644d48..c5e2db4116ea 100644
--- a/doc/api/next_api_changes/deprecations.rst
+++ b/doc/api/next_api_changes/deprecations.rst
@@ -391,3 +391,7 @@ attribute are deprecated.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 This method is deprecated.  Use the ``GridSpec.nrows``, ``GridSpec.ncols``,
 ``SubplotSpec.rowspan``, and ``SubplotSpec.colspan`` properties instead.
+
+Qt4-based backends
+~~~~~~~~~~~~~~~~~~
+The qt4agg and qt4cairo backends are deprecated.
diff --git a/lib/matplotlib/backends/backend_qt4.py b/lib/matplotlib/backends/backend_qt4.py
index b6e38a7a9718..a028a3a32cc9 100644
--- a/lib/matplotlib/backends/backend_qt4.py
+++ b/lib/matplotlib/backends/backend_qt4.py
@@ -1,9 +1,13 @@
+from .. import cbook
 from .backend_qt5 import (
     backend_version, SPECIAL_KEYS, SUPER, ALT, CTRL, SHIFT, MODIFIER_KEYS,
     cursord, _create_qApp, _BackendQT5, TimerQT, MainWindow, FigureCanvasQT,
     FigureManagerQT, NavigationToolbar2QT, SubplotToolQt, exception_handler)
 
 
+cbook.warn_deprecated("3.3", name=__name__, obj_type="backend")
+
+
 @_BackendQT5.export
 class _BackendQT4(_BackendQT5):
     class FigureCanvas(FigureCanvasQT):
diff --git a/lib/matplotlib/backends/backend_qt4agg.py b/lib/matplotlib/backends/backend_qt4agg.py
index 03e7ac920566..0d7048ff3eaf 100644
--- a/lib/matplotlib/backends/backend_qt4agg.py
+++ b/lib/matplotlib/backends/backend_qt4agg.py
@@ -2,10 +2,14 @@
 Render to qt from agg
 """
 
+from .. import cbook
 from .backend_qt5agg import (
     _BackendQT5Agg, FigureCanvasQTAgg, FigureManagerQT, NavigationToolbar2QT)
 
 
+cbook.warn_deprecated("3.3", name=__name__, obj_type="backend")
+
+
 @_BackendQT5Agg.export
 class _BackendQT4Agg(_BackendQT5Agg):
     class FigureCanvas(FigureCanvasQTAgg):
diff --git a/lib/matplotlib/backends/backend_qt4cairo.py b/lib/matplotlib/backends/backend_qt4cairo.py
index f785aa0bd40b..5305c07081c3 100644
--- a/lib/matplotlib/backends/backend_qt4cairo.py
+++ b/lib/matplotlib/backends/backend_qt4cairo.py
@@ -1,6 +1,10 @@
+from .. import cbook
 from .backend_qt5cairo import _BackendQT5Cairo, FigureCanvasQTCairo
 
 
+cbook.warn_deprecated("3.3", name=__name__, obj_type="backend")
+
+
 @_BackendQT5Cairo.export
 class _BackendQT4Cairo(_BackendQT5Cairo):
     class FigureCanvas(FigureCanvasQTCairo):
diff --git a/lib/matplotlib/backends/qt_compat.py b/lib/matplotlib/backends/qt_compat.py
index ca0daa2a0433..eb494dd67ca2 100644
--- a/lib/matplotlib/backends/qt_compat.py
+++ b/lib/matplotlib/backends/qt_compat.py
@@ -9,6 +9,8 @@
   it; i.e. if the Qt5Agg backend is requested but QT_API is set to "pyqt4",
   then actually use Qt5 with PyQt5 or PySide2 (whichever can be imported);
 - otherwise, use whatever the rcParams indicate.
+
+Support for PyQt4 is deprecated.
 """
 
 from distutils.version import LooseVersion
@@ -175,3 +177,6 @@ def is_pyqt5():
 ETS = dict(pyqt=(QT_API_PYQTv2, 4), pyside=(QT_API_PYSIDE, 4),
            pyqt5=(QT_API_PYQT5, 5), pyside2=(QT_API_PYSIDE2, 5))
 QT_RC_MAJOR_VERSION = 5 if is_pyqt5() else 4
+
+if not is_pyqt5():
+    mpl.cbook.warn_deprecated("3.3", name="support for Qt4")