diff --git a/lib/matplotlib/animation.py b/lib/matplotlib/animation.py
index a0236a6956cb..47f2f0f9515b 100644
--- a/lib/matplotlib/animation.py
+++ b/lib/matplotlib/animation.py
@@ -178,6 +178,14 @@ def frame_size(self):
         w, h = self.fig.get_size_inches()
         return int(w * self.dpi), int(h * self.dpi)
 
+    def _supports_transparency(self):
+        """
+        Whether this writer supports transparency.
+
+        Writers may consult output file type and codec to determine this at runtime.
+        """
+        return False
+
     @abc.abstractmethod
     def grab_frame(self, **savefig_kwargs):
         """
@@ -468,6 +476,9 @@ def finish(self):
 
 @writers.register('pillow')
 class PillowWriter(AbstractMovieWriter):
+    def _supports_transparency(self):
+        return True
+
     @classmethod
     def isAvailable(cls):
         return True
@@ -503,11 +514,26 @@ class FFMpegBase:
     _exec_key = 'animation.ffmpeg_path'
     _args_key = 'animation.ffmpeg_args'
 
+    def _supports_transparency(self):
+        suffix = Path(self.outfile).suffix
+        if suffix in {'.apng', '.avif', '.gif', '.webm', '.webp'}:
+            return True
+        # This list was found by going through `ffmpeg -codecs` for video encoders,
+        # running them with _support_transparency() forced to True, and checking that
+        # the "Pixel format" in Kdenlive included alpha. Note this is not a guarantee
+        # that transparency will work; you may also need to pass `-pix_fmt`, but we
+        # trust the user has done so if they are asking for these formats.
+        return self.codec in {
+            'apng', 'avrp', 'bmp', 'cfhd', 'dpx', 'ffv1', 'ffvhuff', 'gif', 'huffyuv',
+            'jpeg2000', 'ljpeg', 'png', 'prores', 'prores_aw', 'prores_ks', 'qtrle',
+            'rawvideo', 'targa', 'tiff', 'utvideo', 'v408', }
+
     @property
     def output_args(self):
         args = []
-        if Path(self.outfile).suffix == '.gif':
-            self.codec = 'gif'
+        suffix = Path(self.outfile).suffix
+        if suffix in {'.apng', '.avif', '.gif', '.webm', '.webp'}:
+            self.codec = suffix[1:]
         else:
             args.extend(['-vcodec', self.codec])
         extra_args = (self.extra_args if self.extra_args is not None
@@ -518,11 +544,17 @@ def output_args(self):
         # macOS). Also fixes internet explorer. This is as of 2015/10/29.
         if self.codec == 'h264' and '-pix_fmt' not in extra_args:
             args.extend(['-pix_fmt', 'yuv420p'])
-        # For GIF, we're telling FFMPEG to split the video stream, to generate
+        # For GIF, we're telling FFmpeg to split the video stream, to generate
         # a palette, and then use it for encoding.
         elif self.codec == 'gif' and '-filter_complex' not in extra_args:
             args.extend(['-filter_complex',
                          'split [a][b];[a] palettegen [p];[b][p] paletteuse'])
+        # For AVIF, we're telling FFmpeg to split the video stream, extract the alpha,
+        # in order to place it in a secondary stream, as needed by AVIF-in-FFmpeg.
+        elif self.codec == 'avif' and '-filter_complex' not in extra_args:
+            args.extend(['-filter_complex',
+                         'split [rgb][rgba]; [rgba] alphaextract [alpha]',
+                         '-map', '[rgb]', '-map', '[alpha]'])
         if self.bitrate > 0:
             args.extend(['-b', '%dk' % self.bitrate])  # %dk: bitrate in kbps.
         for k, v in self.metadata.items():
@@ -610,6 +642,10 @@ class ImageMagickBase:
     _exec_key = 'animation.convert_path'
     _args_key = 'animation.convert_args'
 
+    def _supports_transparency(self):
+        suffix = Path(self.outfile).suffix
+        return suffix in {'.apng', '.avif', '.gif', '.webm', '.webp'}
+
     def _args(self):
         # ImageMagick does not recognize "raw".
         fmt = "rgba" if self.frame_format == "raw" else self.frame_format
@@ -1045,22 +1081,23 @@ def func(current_frame: int, total_frames: int) -> Any
         # since GUI widgets are gone. Either need to remove extra code to
         # allow for this non-existent use case or find a way to make it work.
 
-        facecolor = savefig_kwargs.get('facecolor',
-                                       mpl.rcParams['savefig.facecolor'])
-        if facecolor == 'auto':
-            facecolor = self._fig.get_facecolor()
-
         def _pre_composite_to_white(color):
             r, g, b, a = mcolors.to_rgba(color)
             return a * np.array([r, g, b]) + 1 - a
 
-        savefig_kwargs['facecolor'] = _pre_composite_to_white(facecolor)
-        savefig_kwargs['transparent'] = False   # just to be safe!
         # canvas._is_saving = True makes the draw_event animation-starting
         # callback a no-op; canvas.manager = None prevents resizing the GUI
         # widget (both are likewise done in savefig()).
         with (writer.saving(self._fig, filename, dpi),
               cbook._setattr_cm(self._fig.canvas, _is_saving=True, manager=None)):
+            if not writer._supports_transparency():
+                facecolor = savefig_kwargs.get('facecolor',
+                                               mpl.rcParams['savefig.facecolor'])
+                if facecolor == 'auto':
+                    facecolor = self._fig.get_facecolor()
+                savefig_kwargs['facecolor'] = _pre_composite_to_white(facecolor)
+                savefig_kwargs['transparent'] = False   # just to be safe!
+
             for anim in all_anim:
                 anim._init_draw()  # Clear the initial frame
             frame_number = 0