diff --git a/Lib/fontTools/subset/svg.py b/Lib/fontTools/subset/svg.py
index c1fa00bc2..3fc1524db 100644
--- a/Lib/fontTools/subset/svg.py
+++ b/Lib/fontTools/subset/svg.py
@@ -1,7 +1,111 @@
+import re
+from itertools import groupby
+
 from fontTools.subset.util import _add_method
+from fontTools.misc import etree
 from fontTools import ttLib
 
 
+GID_RE = re.compile("^glyph(\d+)$")
+
+
+XLINK_HREF = "{http://www.w3.org/1999/xlink}href"
+
+
+def remap_glyph_ids(svg, glyph_index_map):
+    id_map = {}
+    href_elements = []
+    for el in svg.iter("*"):
+        # we'll rename these later
+        if XLINK_HREF in el.attrib and el.attrib[XLINK_HREF].startswith("#"):
+            href_elements.append(el)
+
+        el_id = el.attrib.get("id")
+        if el_id is None:
+            continue
+        m = GID_RE.match(el_id)
+        if not m:
+            continue
+        old_index = int(m.group(1))
+        new_index = glyph_index_map.get(old_index)
+        if new_index is not None:
+            if old_index == new_index:
+                continue
+            new_id = f"glyph{new_index}"
+        else:
+            # If the old id is missing, the element correspond to a glyph that was
+            # excluded from the font's subset.
+            # For now we keep it around, renamed to avoid clashes with the new GID
+            # (though technically there could still be clashes even after we insert
+            # a tilde at the beginning, e.g. '~glyphXXX' is still a valid id...).
+            # TODO Figure out how to best prune the SVG document of unused elements.
+            # https://github.com/fonttools/fonttools/issues/534
+            new_id = f"~{el_id}"
+
+        id_map[el_id] = new_id
+        el.attrib["id"] = new_id
+
+    if not id_map:
+        return
+
+    # update xlink:href="#..." that refer to the old id to point to the new one
+    for el in href_elements:
+        ref = el.attrib[XLINK_HREF]
+        # we only care about local #fragment identifiers
+        assert ref.startswith("#")
+        old_id = ref[1:]
+        if old_id in id_map:
+            new_id = id_map[old_id]
+            el.attrib[XLINK_HREF] = f"#{new_id}"
+
+
+def ranges(ints):
+    """Yield (min, max) ranges of consecutive integers from the input set"""
+    sorted_ints = sorted(set(ints))
+    # to group together consecutive ints, we use as 'key' the difference
+    # between their index in the (sorted) list and themselves, which stays
+    # the same for consecutive numbers
+    for _key, group in groupby(enumerate(sorted_ints), lambda i: i[0] - i[1]):
+        consecutive_ints = [v for _i, v in group]
+        yield (consecutive_ints[0], consecutive_ints[-1])
+
+
 @_add_method(ttLib.getTableClass("SVG "))
 def subset_glyphs(self, s):
-    return True  # XXX
+    # ordered list of glyph names (before subsetting)
+    glyph_order = s.orig_glyph_order
+    # map from glyph names to original glyph indices
+    rev_orig_glyph_map = s.reverseOrigGlyphMap
+    # map from original to new glyph indices (after subsetting)
+    glyph_index_map = s.glyph_index_map
+
+    new_docs = []
+    for doc, start_gid, end_gid in self.docList:
+        old_glyphs = {glyph_order[i] for i in range(start_gid, end_gid + 1)}
+        new_glyphs = old_glyphs.intersection(s.glyphs)
+        if not new_glyphs:
+            # no intersection: we can drop the whole record
+            continue
+
+        # NOTE If new_glyphs != old_glyphs, there's only a partial intersection: i.e.
+        # we'll likely end up with unused garbage until we figure out how to prune
+        # the unused refereces from the SVG doc.
+
+        # NOTE huge_tree=True disables security restrictions and support very deep trees
+        # and very long text content. Without it I would get an error like this:
+        # `lxml.etree.XMLSyntaxError: internal error: Huge input lookup`
+        # when parsing noto-emoji-picosvg.svg from googlefonts/color-fonts.
+        # This is lxml-only API, won't work with built-in ElementTree...
+        svg = etree.fromstring(doc, parser=etree.XMLParser(huge_tree=True))
+
+        remap_glyph_ids(svg, glyph_index_map)
+
+        new_doc = etree.tostring(svg)
+
+        new_gids = {glyph_index_map[rev_orig_glyph_map[g]] for g in new_glyphs}
+        for start_gid, end_gid in ranges(new_gids):
+            new_docs.append((new_doc, start_gid, end_gid))
+
+    self.docList = new_docs
+
+    return bool(self.docList)