diff --git a/lib/matplotlib/backends/backend_cairo.py b/lib/matplotlib/backends/backend_cairo.py
@@ -3,12 +3,12 @@
 ==============================
 :Author: Steve Chaplin and others
 
-This backend depends on `cairo <http://cairographics.org>`_, and either on
-cairocffi, or (Python 2 only) on pycairo.
+This backend depends on cairocffi or pycairo.
 """
 
 import six
 
+import copy
 import gzip
 import sys
 import warnings
@@ -35,13 +35,14 @@
                       "cairo>=1.4.0 is required".format(cairo.version))
 backend_version = cairo.version
 
+from matplotlib import cbook
 from matplotlib.backend_bases import (
     _Backend, FigureCanvasBase, FigureManagerBase, GraphicsContextBase,
     RendererBase)
+from matplotlib.font_manager import ttfFontProperty
 from matplotlib.mathtext import MathTextParser
 from matplotlib.path import Path
 from matplotlib.transforms import Affine2D
-from matplotlib.font_manager import ttfFontProperty
 
 
 def _premultiplied_argb32_to_unmultiplied_rgba8888(buf):
@@ -79,6 +80,93 @@ def buffer_info(self):
         return (self.__data, self.__size)
 
 
+# Mapping from Matplotlib Path codes to cairo path codes.
+_MPL_TO_CAIRO_PATH_TYPE = np.zeros(80, dtype=int)  # CLOSEPOLY = 79.
+_MPL_TO_CAIRO_PATH_TYPE[Path.MOVETO] = cairo.PATH_MOVE_TO
+_MPL_TO_CAIRO_PATH_TYPE[Path.LINETO] = cairo.PATH_LINE_TO
+_MPL_TO_CAIRO_PATH_TYPE[Path.CURVE4] = cairo.PATH_CURVE_TO
+_MPL_TO_CAIRO_PATH_TYPE[Path.CLOSEPOLY] = cairo.PATH_CLOSE_PATH
+# Sizes in cairo_path_data_t of each cairo path element.
+_CAIRO_PATH_TYPE_SIZES = np.zeros(4, dtype=int)
+_CAIRO_PATH_TYPE_SIZES[cairo.PATH_MOVE_TO] = 2
+_CAIRO_PATH_TYPE_SIZES[cairo.PATH_LINE_TO] = 2
+_CAIRO_PATH_TYPE_SIZES[cairo.PATH_CURVE_TO] = 4
+_CAIRO_PATH_TYPE_SIZES[cairo.PATH_CLOSE_PATH] = 1
+
+
+def _append_paths_slow(ctx, paths, transforms, clip=None):
+    for path, transform in zip(paths, transforms):
+        for points, code in path.iter_segments(transform, clip=clip):
+            if code == Path.MOVETO:
+                ctx.move_to(*points)
+            elif code == Path.CLOSEPOLY:
+                ctx.close_path()
+            elif code == Path.LINETO:
+                ctx.line_to(*points)
+            elif code == Path.CURVE3:
+                cur = ctx.get_current_point()
+                ctx.curve_to(
+                    *np.concatenate([cur / 3 + points[:2] * 2 / 3,
+                                     points[:2] * 2 / 3 + points[-2:] / 3]))
+            elif code == Path.CURVE4:
+                ctx.curve_to(*points)
+
+
+def _append_paths_fast(ctx, paths, transforms, clip=None):
+    # We directly convert to the internal representation used by cairo, for
+    # which ABI compatibility is guaranteed.  The layout for each item is
+    # --CODE(4)--  -LENGTH(4)-  ---------PAD(8)---------
+    # ----------X(8)----------  ----------Y(8)----------
+    # with the size in bytes in parentheses, and (X, Y) repeated as many times
+    # as there are points for the current code.
+    ffi = cairo.ffi
+
+    # Convert curves to segment, so that 1. we don't have to handle
+    # variable-sized CURVE-n codes, and 2. we don't have to implement degree
+    # elevation for quadratic Beziers.
+    cleaneds = [path.cleaned(transform=transform, clip=clip, curves=False)
+                for path, transform in zip(paths, transforms)]
+    vertices = np.concatenate([cleaned.vertices for cleaned in cleaneds])
+    codes = np.concatenate([cleaned.codes for cleaned in cleaneds])
+
+    # Remove unused vertices and convert to cairo codes.  Note that unlike
+    # cairo_close_path, we do not explicitly insert an extraneous MOVE_TO after
+    # CLOSE_PATH, so our resulting buffer may be smaller.
+    vertices = vertices[(codes != Path.STOP) & (codes != Path.CLOSEPOLY)]
+    codes = codes[codes != Path.STOP]
+    codes = _MPL_TO_CAIRO_PATH_TYPE[codes]
+
+    # Where are the headers of each cairo portions?
+    cairo_type_sizes = _CAIRO_PATH_TYPE_SIZES[codes]
+    cairo_type_positions = np.insert(np.cumsum(cairo_type_sizes), 0, 0)
+    cairo_num_data = cairo_type_positions[-1]
+    cairo_type_positions = cairo_type_positions[:-1]
+
+    # Fill the buffer.
+    buf = np.empty(cairo_num_data * 16, np.uint8)
+    as_int = np.frombuffer(buf.data, np.int32)
+    as_int[::4][cairo_type_positions] = codes
+    as_int[1::4][cairo_type_positions] = cairo_type_sizes
+    as_float = np.frombuffer(buf.data, np.float64)
+    mask = np.ones_like(as_float, bool)
+    mask[::2][cairo_type_positions] = mask[1::2][cairo_type_positions] = False
+    as_float[mask] = vertices.ravel()
+
+    # Construct the cairo_path_t, and pass it to the context.
+    ptr = ffi.new("cairo_path_t *")
+    ptr.status = cairo.STATUS_SUCCESS
+    ptr.data = ffi.cast("cairo_path_data_t *", ffi.from_buffer(buf))
+    ptr.num_data = cairo_num_data
+    cairo.cairo.cairo_append_path(ctx._pointer, ptr)
+
+
+_append_paths = _append_paths_fast if HAS_CAIRO_CFFI else _append_paths_slow
+
+
+def _append_path(ctx, path, transform, clip=None):
+    return _append_paths(ctx, [path], [transform], clip)
+
+
 class RendererCairo(RendererBase):
     fontweights = {
         100          : cairo.FONT_WEIGHT_NORMAL,
@@ -139,37 +227,20 @@ def _fill_and_stroke(self, ctx, fill_c, alpha, alpha_overrides):
         ctx.stroke()
 
     @staticmethod
+    @cbook.deprecated("3.0")
     def convert_path(ctx, path, transform, clip=None):
-        for points, code in path.iter_segments(transform, clip=clip):
-            if code == Path.MOVETO:
-                ctx.move_to(*points)
-            elif code == Path.CLOSEPOLY:
-                ctx.close_path()
-            elif code == Path.LINETO:
-                ctx.line_to(*points)
-            elif code == Path.CURVE3:
-                ctx.curve_to(points[0], points[1],
-                             points[0], points[1],
-                             points[2], points[3])
-            elif code == Path.CURVE4:
-                ctx.curve_to(*points)
+        _append_path(ctx, path, transform, clip)
 
     def draw_path(self, gc, path, transform, rgbFace=None):
         ctx = gc.ctx
-
-        # We'll clip the path to the actual rendering extents
-        # if the path isn't filled.
-        if rgbFace is None and gc.get_hatch() is None:
-            clip = ctx.clip_extents()
-        else:
-            clip = None
-
+        # Clip the path to the actual rendering extents if it isn't filled.
+        clip = (ctx.clip_extents()
+                if rgbFace is None and gc.get_hatch() is None
+                else None)
         transform = (transform
-                     + Affine2D().scale(1.0, -1.0).translate(0, self.height))
-
+                     + Affine2D().scale(1, -1).translate(0, self.height))
         ctx.new_path()
-        self.convert_path(ctx, path, transform, clip)
-
+        _append_path(ctx, path, transform, clip)
         self._fill_and_stroke(
             ctx, rgbFace, gc.get_alpha(), gc.get_forced_alpha())
 
@@ -179,8 +250,7 @@ def draw_markers(self, gc, marker_path, marker_trans, path, transform,
 
         ctx.new_path()
         # Create the path for the marker; it needs to be flipped here already!
-        self.convert_path(
-            ctx, marker_path, marker_trans + Affine2D().scale(1.0, -1.0))
+        _append_path(ctx, marker_path, marker_trans + Affine2D().scale(1, -1))
         marker_path = ctx.copy_path_flat()
 
         # Figure out whether the path has a fill
@@ -193,7 +263,7 @@ def draw_markers(self, gc, marker_path, marker_trans, path, transform,
             filled = True
 
         transform = (transform
-                     + Affine2D().scale(1.0, -1.0).translate(0, self.height))
+                     + Affine2D().scale(1, -1).translate(0, self.height))
 
         ctx.new_path()
         for i, (vertices, codes) in enumerate(
@@ -221,6 +291,57 @@ def draw_markers(self, gc, marker_path, marker_trans, path, transform,
             self._fill_and_stroke(
                 ctx, rgbFace, gc.get_alpha(), gc.get_forced_alpha())
 
+    def draw_path_collection(
+            self, gc, master_transform, paths, all_transforms, offsets,
+            offsetTrans, facecolors, edgecolors, linewidths, linestyles,
+            antialiaseds, urls, offset_position):
+
+        path_ids = []
+        for path, transform in self._iter_collection_raw_paths(
+                master_transform, paths, all_transforms):
+            path_ids.append((path, Affine2D(transform)))
+
+        reuse_key = None
+        grouped_draw = []
+
+        def _draw_paths():
+            if not grouped_draw:
+                return
+            gc_vars, rgb_fc = reuse_key
+            gc = copy.copy(gc0)
+            # We actually need to call the setters to reset the internal state.
+            vars(gc).update(gc_vars)
+            for k, v in gc_vars.items():
+                if k == "_linestyle":  # Deprecated, no effect.
+                    continue
+                try:
+                    getattr(gc, "set" + k)(v)
+                except (AttributeError, TypeError) as e:
+                    pass
+            gc.ctx.new_path()
+            paths, transforms = zip(*grouped_draw)
+            grouped_draw.clear()
+            _append_paths(gc.ctx, paths, transforms)
+            self._fill_and_stroke(
+                gc.ctx, rgb_fc, gc.get_alpha(), gc.get_forced_alpha())
+
+        for xo, yo, path_id, gc0, rgb_fc in self._iter_collection(
+                gc, master_transform, all_transforms, path_ids, offsets,
+                offsetTrans, facecolors, edgecolors, linewidths, linestyles,
+                antialiaseds, urls, offset_position):
+            path, transform = path_id
+            transform = (Affine2D(transform.get_matrix())
+                         .translate(xo, yo - self.height).scale(1, -1))
+            # rgb_fc could be a ndarray, for which equality is elementwise.
+            new_key = vars(gc0), tuple(rgb_fc) if rgb_fc is not None else None
+            if new_key == reuse_key:
+                grouped_draw.append((path, transform))
+            else:
+                _draw_paths()
+                grouped_draw.append((path, transform))
+                reuse_key = new_key
+        _draw_paths()
+
     def draw_image(self, gc, x, y, im):
         # bbox - not currently used
         if sys.byteorder == 'little':
@@ -233,12 +354,12 @@ def draw_image(self, gc, x, y, im):
             # on ctypes to get a pointer to the numpy array. This works
             # correctly on a numpy array in python3 but not 2.7. We replicate
             # the array.array functionality here to get cross version support.
-            imbuffer = ArrayWrapper(im.flatten())
+            imbuffer = ArrayWrapper(im.ravel())
         else:
-            # pycairo uses PyObject_AsWriteBuffer to get a pointer to the
+            # py2cairo uses PyObject_AsWriteBuffer to get a pointer to the
             # numpy array; this works correctly on a regular numpy array but
-            # not on a py2 memoryview.
-            imbuffer = im.flatten()
+            # not on a memory view.
+            imbuffer = im.ravel()
         surface = cairo.ImageSurface.create_for_data(
             imbuffer, cairo.FORMAT_ARGB32,
             im.shape[1], im.shape[0], im.shape[1]*4)
@@ -247,7 +368,7 @@ def draw_image(self, gc, x, y, im):
 
         ctx.save()
         ctx.set_source_surface(surface, float(x), float(y))
-        if gc.get_alpha() != 1.0:
+        if gc.get_alpha() != 1:
             ctx.paint_with_alpha(gc.get_alpha())
         else:
             ctx.paint()
@@ -299,7 +420,6 @@ def _draw_mathtext(self, gc, x, y, s, prop, angle):
             ctx.move_to(ox, oy)
 
             fontProp = ttfFontProperty(font)
-            ctx.save()
             ctx.select_font_face(fontProp.name,
                                  self.fontangles[fontProp.style],
                                  self.fontweights[fontProp.weight])
@@ -309,7 +429,6 @@ def _draw_mathtext(self, gc, x, y, s, prop, angle):
             if not six.PY3 and isinstance(s, six.text_type):
                 s = s.encode("utf-8")
             ctx.show_text(s)
-            ctx.restore()
 
         for ox, oy, w, h in rects:
             ctx.new_path()
@@ -415,7 +534,7 @@ def set_clip_path(self, path):
         ctx.new_path()
         affine = (affine
                   + Affine2D().scale(1, -1).translate(0, self.renderer.height))
-        RendererCairo.convert_path(ctx, tpath, affine)
+        _append_path(ctx, tpath, affine)
         ctx.clip()
 
     def set_dashes(self, offset, dashes):