diff --git a/branca/element.py b/branca/element.py
index 853ca16..504e7cc 100644
--- a/branca/element.py
+++ b/branca/element.py
@@ -328,7 +328,8 @@ class Figure(Element):
         A percentage defining the aspect ratio of the Figure.
         It will be ignored if height is not None.
     title : str, default None
-        Figure title.
+        Figure title. Also used as the ``title`` attribute (accessible
+        name) of the iframe when the Figure is displayed in a notebook.
     figsize : tuple of two int, default None
         If you're a matplotlib addict, you can overwrite width and
         height. Values will be converted into pixels in using 60 dpi.
@@ -412,24 +413,37 @@ def render(self, **kwargs) -> str:
     def _repr_html_(self, **kwargs) -> str:
         """Displays the Figure in a Jupyter notebook."""
         html = escape(self.render(**kwargs))
+        # Give the iframe an accessible name when a title is set, so it is
+        # not flagged by "frames must have an accessible name" audits.
+        title_attr = f' title="{escape(self.title)}"' if self.title else ""
         if self.height is None:
             iframe = (
                 '<div style="width:{width};">'
                 '<div style="position:relative;width:100%;height:0;padding-bottom:{ratio};">'  # noqa
                 '<span style="color:#565656">Make this Notebook Trusted to load map: File -> Trust Notebook</span>'  # noqa
-                '<iframe srcdoc="{html}" style="position:absolute;width:100%;height:100%;left:0;top:0;'  # noqa
+                '<iframe srcdoc="{html}"{title_attr} style="position:absolute;width:100%;height:100%;left:0;top:0;'  # noqa
                 'border:none !important;" '
                 "allowfullscreen webkitallowfullscreen mozallowfullscreen>"
                 "</iframe>"
                 "</div></div>"
-            ).format(html=html, width=self.width, ratio=self.ratio)
+            ).format(
+                html=html,
+                width=self.width,
+                ratio=self.ratio,
+                title_attr=title_attr,
+            )
         else:
             iframe = (
-                '<iframe srcdoc="{html}" width="{width}" height="{height}"'
+                '<iframe srcdoc="{html}"{title_attr} width="{width}" height="{height}" '
                 'style="border:none !important;" '
-                '"allowfullscreen" "webkitallowfullscreen" "mozallowfullscreen">'
+                "allowfullscreen webkitallowfullscreen mozallowfullscreen>"
                 "</iframe>"
-            ).format(html=html, width=self.width, height=self.height)
+            ).format(
+                html=html,
+                width=self.width,
+                height=self.height,
+                title_attr=title_attr,
+            )
         return iframe
 
     def add_subplot(self, x: int, y: int, n: int, margin: float = 0.05) -> "Div":
@@ -640,6 +654,10 @@ class IFrame(Element):
         height. Values will be converted into pixels in using 60 dpi.
         For example figsize=(10, 5) will result in
         width="600px", height="300px".
+    title : str, default None
+        Value for the iframe's ``title`` attribute, used as the frame's
+        accessible name. Set it to satisfy accessibility audits that
+        require every frame to have an accessible name.
     """
 
     def __init__(
@@ -649,10 +667,12 @@ def __init__(
         height: Optional[str] = None,
         ratio: str = "60%",
         figsize: Optional[Tuple[int, int]] = None,
+        title: Optional[str] = None,
     ):
         super().__init__()
         self._name = "IFrame"
 
+        self.title = title
         self.width = width
         self.height = height
         self.ratio = ratio
@@ -671,21 +691,32 @@ def render(self, **kwargs) -> str:
         html = "data:text/html;charset=utf-8;base64," + base64.b64encode(
             html.encode("utf8"),
         ).decode("utf8")
+        title_attr = f' title="{escape(self.title)}"' if self.title else ""
 
         if self.height is None:
             iframe = (
                 '<div style="width:{width};">'
                 '<div style="position:relative;width:100%;height:0;padding-bottom:{ratio};">'  # noqa
-                '<iframe src="{html}" style="position:absolute;width:100%;height:100%;left:0;top:0;'  # noqa
+                '<iframe src="{html}"{title_attr} style="position:absolute;width:100%;height:100%;left:0;top:0;'  # noqa
                 'border:none !important;">'
                 "</iframe>"
                 "</div></div>"
-            ).format(html=html, width=self.width, ratio=self.ratio)
+            ).format(
+                html=html,
+                width=self.width,
+                ratio=self.ratio,
+                title_attr=title_attr,
+            )
         else:
             iframe = (
-                '<iframe src="{html}" width="{width}" style="border:none !important;" '
+                '<iframe src="{html}"{title_attr} width="{width}" style="border:none !important;" '
                 'height="{height}"></iframe>'
-            ).format(html=html, width=self.width, height=self.height)
+            ).format(
+                html=html,
+                width=self.width,
+                height=self.height,
+                title_attr=title_attr,
+            )
         return iframe
 
 
diff --git a/tests/test_element.py b/tests/test_element.py
new file mode 100644
index 0000000..934703a
--- /dev/null
+++ b/tests/test_element.py
@@ -0,0 +1,76 @@
+"""
+Tests for branca.element
+------------------------
+"""
+
+from html.parser import HTMLParser
+
+import branca.element as elem
+
+
+class _IframeAttrs(HTMLParser):
+    """Collect the attributes of every <iframe> start tag."""
+
+    def __init__(self):
+        super().__init__()
+        self.iframes = []
+
+    def handle_starttag(self, tag, attrs):
+        if tag == "iframe":
+            self.iframes.append(dict(attrs))
+
+
+def _iframe_attrs(html):
+    parser = _IframeAttrs()
+    parser.feed(html)
+    assert len(parser.iframes) == 1
+    return parser.iframes[0]
+
+
+def test_figure_repr_html_fullscreen_attrs_without_height():
+    attrs = _iframe_attrs(elem.Figure()._repr_html_())
+    for name in ("allowfullscreen", "webkitallowfullscreen", "mozallowfullscreen"):
+        assert name in attrs
+
+
+def test_figure_repr_html_fullscreen_attrs_with_height():
+    # The height branch used to quote the boolean attributes, producing
+    # <iframe ... "allowfullscreen" ...>, so the attribute names came out
+    # wrapped in literal quotes and the browser ignored them.
+    attrs = _iframe_attrs(elem.Figure(height="400px")._repr_html_())
+    for name in ("allowfullscreen", "webkitallowfullscreen", "mozallowfullscreen"):
+        assert name in attrs, f"{name!r} missing; got {sorted(attrs)}"
+    assert attrs["height"] == "400px"
+    assert attrs["width"] == "100%"
+
+
+def test_figure_iframe_title_absent_by_default():
+    for height in (None, "400px"):
+        attrs = _iframe_attrs(elem.Figure(height=height)._repr_html_())
+        assert "title" not in attrs
+
+
+def test_figure_iframe_title_set():
+    for height in (None, "400px"):
+        attrs = _iframe_attrs(elem.Figure(height=height, title="My Map")._repr_html_())
+        assert attrs["title"] == "My Map"
+
+
+def test_figure_iframe_title_is_escaped():
+    # A title with a double quote must not break out of the attribute.
+    attrs = _iframe_attrs(elem.Figure(title='a "b" <c>')._repr_html_())
+    assert attrs["title"] == 'a "b" <c>'
+
+
+def test_iframe_title_absent_by_default():
+    for height in (None, "300px"):
+        attrs = _iframe_attrs(elem.IFrame("<p>x</p>", height=height).render())
+        assert "title" not in attrs
+
+
+def test_iframe_title_set():
+    for height in (None, "300px"):
+        attrs = _iframe_attrs(
+            elem.IFrame("<p>x</p>", height=height, title="Popup").render(),
+        )
+        assert attrs["title"] == "Popup"