diff --git a/myst_nb/core/nb_to_tokens.py b/myst_nb/core/nb_to_tokens.py
index c8e48f03..59448334 100644
--- a/myst_nb/core/nb_to_tokens.py
+++ b/myst_nb/core/nb_to_tokens.py
@@ -48,6 +48,7 @@ def notebook_to_tokens(
 
         # generate tokens
         tokens: list[Token]
+        cell_id = nb_cell.get("id", None)
         if nb_cell["cell_type"] == "markdown":
             # https://nbformat.readthedocs.io/en/5.1.3/format_description.html#markdown-cells
             # TODO if cell has tag output-caption, then use as caption for next/preceding cell?
@@ -60,6 +61,7 @@ def notebook_to_tokens(
                     meta={
                         "index": cell_index,
                         "metadata": nb_node_to_dict(nb_cell["metadata"]),
+                        "id": cell_id,
                     },
                     map=[0, len(nb_cell["source"].splitlines()) - 1],
                 ),
@@ -88,6 +90,7 @@ def notebook_to_tokens(
                     meta={
                         "index": cell_index,
                         "metadata": nb_node_to_dict(nb_cell["metadata"]),
+                        "id": cell_id,
                     },
                     map=[0, 0],
                 )
@@ -106,6 +109,7 @@ def notebook_to_tokens(
                     meta={
                         "index": cell_index,
                         "metadata": nb_node_to_dict(nb_cell["metadata"]),
+                        "id": cell_id,
                     },
                     map=[0, 0],
                 )
diff --git a/myst_nb/core/read.py b/myst_nb/core/read.py
index 2b3dae4b..56609097 100644
--- a/myst_nb/core/read.py
+++ b/myst_nb/core/read.py
@@ -31,6 +31,8 @@ class NbReader:
     """The configuration for parsing markdown cells."""
     read_fmt: dict | None = dc.field(default=None)
     """The type of the reader, if known."""
+    support_cell_ids: bool = False
+    """Whether the format supports stable cell IDs"""
 
 
 def standard_nb_read(text: str) -> nbf.NotebookNode:
@@ -75,7 +77,11 @@ def create_nb_reader(
             if commonmark_only:
                 # Markdown cells should be read as Markdown only
                 md_config = dc.replace(md_config, commonmark_only=True)
-            return NbReader(partial(reader, **(reader_kwargs or {})), md_config)  # type: ignore
+            return NbReader(
+                partial(reader, **(reader_kwargs or {})),  # type: ignore
+                md_config,
+                support_cell_ids=suffix == ".ipynb",
+            )
 
     # a Markdown file is a special case, since we only treat it as a notebook,
     # if it starts with certain "top-matter"
@@ -89,6 +95,7 @@ def create_nb_reader(
             ),
             md_config,
             {"type": "plugin", "name": "myst_nb_md"},
+            support_cell_ids=False,
         )
 
     # if we get here, we did not find a reader
diff --git a/myst_nb/core/render.py b/myst_nb/core/render.py
index 14b82816..5baecf85 100644
--- a/myst_nb/core/render.py
+++ b/myst_nb/core/render.py
@@ -64,6 +64,7 @@ class MditRenderMixin:
     current_node: Any
     current_node_context: Any
     create_highlighted_code_block: Any
+    _heading_slugs: Any  # TODO create & expose a method in `DocutilsRenderer`
 
     @property
     def nb_config(self: SelfType) -> NbParserConfig:
@@ -179,6 +180,17 @@ def render_nb_cell_code(self: SelfType, token: SyntaxTreeNode) -> None:
             cell_metadata=token.meta["metadata"],
             classes=classes,
         )
+
+        cell_id = token.meta["id"]
+        if cell_id and not cell_id.startswith("RANDOM_CELL_ID"):
+            self.document.note_implicit_target(cell_container, cell_container)
+            slug = "cell-id=" + cell_id
+            cell_container["slug"] = slug
+            self._heading_slugs[slug] = (
+                cell_container.line,
+                cell_container["ids"][0],
+                "",
+            )
         if hide_mode:
             cell_container["hide_mode"] = hide_mode
             code_prompt_show = self.get_cell_level_config(
diff --git a/myst_nb/sphinx_.py b/myst_nb/sphinx_.py
index 4885d9ff..e3598622 100644
--- a/myst_nb/sphinx_.py
+++ b/myst_nb/sphinx_.py
@@ -88,6 +88,12 @@ def parse(self, inputstring: str, document: nodes.document) -> None:
             return super().parse(inputstring, document)
         notebook = nb_reader.read(inputstring)
 
+        if not nb_reader.support_cell_ids:
+            # mark randomly generated cell IDs
+            for cell in notebook["cells"]:
+                if "id" in cell:
+                    cell["id"] = "RANDOM_CELL_ID_" + cell["id"]
+
         # update the global markdown config with the file-level config
         warning = lambda wtype, msg: create_warning(  # noqa: E731
             document, msg, line=1, append_to=document, subtype=wtype