diff --git a/Cargo.lock b/Cargo.lock
index 79b7d92425a7e..7bf9527f47d12 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -619,7 +619,7 @@ dependencies = [
  "clippy_utils",
  "if_chain",
  "itertools 0.10.1",
- "pulldown-cmark",
+ "pulldown-cmark 0.9.0",
  "quine-mc_cluskey",
  "regex-syntax",
  "rustc-semver",
@@ -2154,7 +2154,7 @@ dependencies = [
  "log",
  "memchr",
  "opener",
- "pulldown-cmark",
+ "pulldown-cmark 0.8.0",
  "regex",
  "serde",
  "serde_derive",
@@ -2813,6 +2813,17 @@ dependencies = [
  "unicase",
 ]
 
+[[package]]
+name = "pulldown-cmark"
+version = "0.9.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "acd16514d1af5f7a71f909a44ef253cdb712a376d7ebc8ae4a471a9be9743548"
+dependencies = [
+ "bitflags",
+ "memchr",
+ "unicase",
+]
+
 [[package]]
 name = "punycode"
 version = "0.4.1"
@@ -4615,7 +4626,7 @@ dependencies = [
  "expect-test",
  "itertools 0.9.0",
  "minifier",
- "pulldown-cmark",
+ "pulldown-cmark 0.9.0",
  "rayon",
  "regex",
  "rustdoc-json-types",
diff --git a/src/librustdoc/Cargo.toml b/src/librustdoc/Cargo.toml
index 3c9b6f5006d59..a3cb982f277a0 100644
--- a/src/librustdoc/Cargo.toml
+++ b/src/librustdoc/Cargo.toml
@@ -8,7 +8,7 @@ path = "lib.rs"
 
 [dependencies]
 arrayvec = { version = "0.7", default-features = false }
-pulldown-cmark = { version = "0.8", default-features = false }
+pulldown-cmark = { version = "0.9", default-features = false }
 minifier = "0.0.41"
 rayon = "1.3.1"
 serde = { version = "1.0", features = ["derive"] }
diff --git a/src/librustdoc/html/markdown.rs b/src/librustdoc/html/markdown.rs
index 545b409175ee6..3fd9c0a194485 100644
--- a/src/librustdoc/html/markdown.rs
+++ b/src/librustdoc/html/markdown.rs
@@ -538,7 +538,7 @@ impl<'a, 'b, 'ids, I: Iterator<Item = SpannedEvent<'a>>> Iterator
         }
 
         let event = self.inner.next();
-        if let Some((Event::Start(Tag::Heading(level)), _)) = event {
+        if let Some((Event::Start(Tag::Heading(level, _, _)), _)) = event {
             let mut id = String::new();
             for event in &mut self.inner {
                 match &event.0 {
@@ -560,7 +560,8 @@ impl<'a, 'b, 'ids, I: Iterator<Item = SpannedEvent<'a>>> Iterator
                 self.buf.push_front((Event::Html(format!("{} ", sec).into()), 0..0));
             }
 
-            let level = std::cmp::min(level + (self.heading_offset as u32), MAX_HEADER_LEVEL);
+            let level =
+                std::cmp::min(level as u32 + (self.heading_offset as u32), MAX_HEADER_LEVEL);
             self.buf.push_back((Event::Html(format!("</a></h{}>", level).into()), 0..0));
 
             let start_tags = format!(
@@ -773,7 +774,7 @@ crate fn find_testable_code<T: doctest::Tester>(
                 tests.add_test(text, block_info, line);
                 prev_offset = offset.start;
             }
-            Event::Start(Tag::Heading(level)) => {
+            Event::Start(Tag::Heading(level, _, _)) => {
                 register_header = Some(level as u32);
             }
             Event::Text(ref s) if register_header.is_some() => {
@@ -1053,7 +1054,7 @@ impl Markdown<'_> {
         let mut replacer = |broken_link: BrokenLink<'_>| {
             links
                 .iter()
-                .find(|link| &*link.original_text == broken_link.reference)
+                .find(|link| link.original_text.as_str() == &*broken_link.reference)
                 .map(|link| (link.href.as_str().into(), link.new_text.as_str().into()))
         };
 
@@ -1134,7 +1135,7 @@ impl MarkdownSummaryLine<'_> {
         let mut replacer = |broken_link: BrokenLink<'_>| {
             links
                 .iter()
-                .find(|link| &*link.original_text == broken_link.reference)
+                .find(|link| link.original_text.as_str() == &*broken_link.reference)
                 .map(|link| (link.href.as_str().into(), link.new_text.as_str().into()))
         };
 
@@ -1168,7 +1169,7 @@ fn markdown_summary_with_limit(
     let mut replacer = |broken_link: BrokenLink<'_>| {
         link_names
             .iter()
-            .find(|link| &*link.original_text == broken_link.reference)
+            .find(|link| link.original_text.as_str() == &*broken_link.reference)
             .map(|link| (link.href.as_str().into(), link.new_text.as_str().into()))
     };
 
@@ -1311,10 +1312,10 @@ crate fn markdown_links(md: &str) -> Vec<MarkdownLink> {
     };
 
     let mut push = |link: BrokenLink<'_>| {
-        let span = span_for_link(&CowStr::Borrowed(link.reference), link.span);
+        let span = span_for_link(&link.reference, link.span);
         links.borrow_mut().push(MarkdownLink {
             kind: LinkType::ShortcutUnknown,
-            link: link.reference.to_owned(),
+            link: link.reference.to_string(),
             range: span,
         });
         None
diff --git a/src/tools/clippy/clippy_lints/Cargo.toml b/src/tools/clippy/clippy_lints/Cargo.toml
index 0661c2803864c..7d2a3e4f639c3 100644
--- a/src/tools/clippy/clippy_lints/Cargo.toml
+++ b/src/tools/clippy/clippy_lints/Cargo.toml
@@ -13,7 +13,7 @@ cargo_metadata = "0.14"
 clippy_utils = { path = "../clippy_utils" }
 if_chain = "1.0"
 itertools = "0.10"
-pulldown-cmark = { version = "0.8", default-features = false }
+pulldown-cmark = { version = "0.9", default-features = false }
 quine-mc_cluskey = "0.2"
 regex-syntax = "0.6"
 serde = { version = "1.0", features = ["derive"] }
diff --git a/src/tools/clippy/clippy_lints/src/doc.rs b/src/tools/clippy/clippy_lints/src/doc.rs
index 3650e4f91a001..7c2717733578b 100644
--- a/src/tools/clippy/clippy_lints/src/doc.rs
+++ b/src/tools/clippy/clippy_lints/src/doc.rs
@@ -542,16 +542,16 @@ fn check_doc<'a, Events: Iterator<Item = (pulldown_cmark::Event<'a>, Range<usize
             },
             Start(Link(_, url, _)) => in_link = Some(url),
             End(Link(..)) => in_link = None,
-            Start(Heading(_) | Paragraph | Item) => {
-                if let Start(Heading(_)) = event {
+            Start(Heading(_, _, _) | Paragraph | Item) => {
+                if let Start(Heading(_, _, _)) = event {
                     in_heading = true;
                 }
                 ticks_unbalanced = false;
                 let (_, span) = get_current_span(spans, range.start);
                 paragraph_span = first_line_of_span(cx, span);
             },
-            End(Heading(_) | Paragraph | Item) => {
-                if let End(Heading(_)) = event {
+            End(Heading(_, _, _) | Paragraph | Item) => {
+                if let End(Heading(_, _, _)) = event {
                     in_heading = false;
                 }
                 if ticks_unbalanced {