diff --git a/tket/src/passes.rs b/tket/src/passes.rs
index 432770e9a..fc8683eba 100644
--- a/tket/src/passes.rs
+++ b/tket/src/passes.rs
@@ -13,4 +13,6 @@ pub use chunks::CircuitChunks;
 pub mod guppy;
 pub use guppy::NormalizeGuppy;
 
+pub mod inline;
+
 pub mod unpack_container;
diff --git a/tket/src/passes/inline.rs b/tket/src/passes/inline.rs
new file mode 100644
index 000000000..db5b32822
--- /dev/null
+++ b/tket/src/passes/inline.rs
@@ -0,0 +1,348 @@
+//! Pass to inline calls to functions, controlled by [InlineAnnotation] metadata.
+use std::collections::{HashMap, HashSet, VecDeque};
+
+use hugr::hugr::patch::inline_call::InlineCallError;
+use hugr::hugr::patch::{Patch, inline_call::InlineCall};
+use hugr_core::module_graph::{ModuleGraph, StaticNode};
+use hugr_core::{Node, hugr::hugrmut::HugrMut, metadata::Metadata};
+use hugr_passes::{ComposablePass, InScope, PassScope, composable::WithScope};
+
+use itertools::Itertools;
+use petgraph::algo::tarjan_scc;
+use petgraph::data::DataMap;
+use petgraph::visit::{
+    Dfs, IntoNeighbors, IntoNodeIdentifiers, IntoNodeReferences, NodeFiltered, NodeIndexable,
+    Visitable, Walker,
+};
+use serde::{Deserialize, Serialize};
+
+/// Annotation that may be applied to functions to indicate
+/// that/when calls to it should be inlined.
+#[derive(Serialize, Deserialize, Debug, Default, Clone, PartialEq, Eq)]
+#[non_exhaustive]
+pub enum InlineAnnotation {
+    /// Always inline calls to this function.
+    ///
+    /// If this cannot be done, an error will be raised.
+    Always,
+    /// Leave inlining to the discretion of the optimizer.
+    #[default]
+    Auto,
+}
+
+impl Metadata for InlineAnnotation {
+    type Type<'hugr> = InlineAnnotation;
+
+    const KEY: &'static str = "tket.inline";
+}
+
+/// Errors that may be raised by [InlinePass]
+#[derive(Clone, Debug, PartialEq, Eq, derive_more::Display)]
+pub enum InlineError<N = Node> {
+    /// Functions annotated with [InlineAnnotation::Always] form a cycle
+    /// so inlining would produce an infinitely-big program
+    #[display("Cycle detected in functions marked to Always inline: {_0:?}")]
+    AlwaysCycle(Vec<N>),
+}
+
+impl<N: std::fmt::Debug> std::error::Error for InlineError<N> {}
+
+/// A [ComposablePass] that inlines `Call`s to functions
+/// according to [InlineAnnotation]s.
+#[derive(Default, Clone, Debug)]
+pub struct InlinePass {
+    scope: PassScope,
+}
+
+impl WithScope for InlinePass {
+    fn with_scope(self, scope: impl Into<PassScope>) -> Self {
+        Self {
+            scope: scope.into(),
+        }
+    }
+}
+
+impl<H: HugrMut> ComposablePass<H> for InlinePass {
+    type Error = InlineError<H::Node>;
+    type Result = ();
+
+    fn run(&self, hugr: &mut H) -> Result<(), InlineError<H::Node>> {
+        let Some(root) = self.scope.root(hugr) else {
+            return Ok(()); // Nothing to do
+        };
+        let cg = ModuleGraph::new(hugr);
+        let reachable_always = {
+            let filter_reachable = match &self.scope {
+                PassScope::Global(_) => None,
+                PassScope::EntrypointFlat | PassScope::EntrypointRecursive => Some(
+                    Dfs::new(cg.graph(), cg.node_index(hugr.entrypoint()).unwrap())
+                        .iter(&cg.graph())
+                        .collect::<Vec<_>>(),
+                ),
+                p => todo!("Update to handle new {p:?}"),
+            };
+            hugr.children(hugr.module_root())
+                .filter_map(|n| cg.node_index(n).map(|ni| (n, ni)))
+                .filter(|(_, ni)| {
+                    filter_reachable
+                        .as_ref()
+                        .is_none_or(|reachable| reachable.contains(ni))
+                })
+                .filter(|(n, _)| {
+                    hugr.get_optype(*n).is_func_defn()
+                        && hugr
+                            .get_metadata::<InlineAnnotation>(*n)
+                            .unwrap_or_default()
+                            == InlineAnnotation::Always
+                })
+                .collect::<HashMap<_, _>>()
+        };
+
+        // If we inverted the map, we'd save a little here, but it'd get much worse in the reverse lookup below
+        if let Some(cycle) = cycles(&NodeFiltered::from_fn(cg.graph(), |n| {
+            match cg.graph().node_weight(n).unwrap() {
+                StaticNode::FuncDefn(func) => reachable_always.contains_key(func),
+                _ => false,
+            }
+        }))
+        .next()
+        {
+            return Err(InlineError::AlwaysCycle(cycle));
+        }
+        let mut parents = VecDeque::from([root]);
+        let mut seen = HashSet::new();
+        while let Some(parent) = parents.pop_front() {
+            if hugr.get_optype(parent).is_func_defn() {
+                seen.insert(parent);
+            }
+            let mut to_inline = Vec::new();
+            for child in hugr.children(parent) {
+                if hugr.first_child(child).is_some() {
+                    parents.push_back(child);
+                } else if hugr.get_optype(child).is_call()
+                    && let Some(func) = hugr.static_source(child)
+                    && reachable_always.contains_key(&func)
+                {
+                    to_inline.push((child, func));
+                }
+            }
+            while let Some((call, func)) = to_inline.pop() {
+                do_inline(call, hugr);
+                // We have not inlined everything into `func` yet, so there may still be some work to do in the inlined copy.
+                // (Inlining in postorder traversal order would avoid this for PassScope::Global,
+                // but we cannot do that for PassScope::EntrypointFlat/Recursive, as there we cannot
+                // touch the functions until they are inlined into the entrypoint-subtree.)
+                if !seen.contains(&func) {
+                    parents.push_back(call);
+                }
+            }
+        }
+        // Also inline any function called only once.
+        // First remove the always-inlined functions themselves, as they are now unreachable.
+        let funcs_to_preserve = self.scope.preserve_interface(hugr).collect::<HashSet<_>>();
+        if root == hugr.module_root() {
+            for func in reachable_always.keys() {
+                if !funcs_to_preserve.contains(func) {
+                    hugr.remove_subtree(*func);
+                }
+            }
+        }
+        let cg = ModuleGraph::new(hugr);
+        let funcs_in_cycles = cycles(cg.graph()).flatten().collect::<HashSet<_>>();
+
+        let called_once = cg
+            .graph()
+            .node_references()
+            .filter_map(|(_, sn)| match sn {
+                StaticNode::FuncDefn(func)
+                    if !funcs_to_preserve.contains(func) && !funcs_in_cycles.contains(func) =>
+                {
+                    hugr.static_targets(*func)
+                        .unwrap()
+                        .exactly_one()
+                        .ok()
+                        .map(|(call, _port)| (*func, call))
+                }
+
+                _ => None,
+            })
+            .collect::<Vec<_>>();
+        for (func, call) in called_once {
+            if hugr.get_optype(call).is_call() // skip LoadFunctions
+                && self.scope.in_scope(hugr, call) != InScope::No
+            {
+                do_inline(call, hugr);
+                if self.scope.in_scope(hugr, func) == InScope::Yes {
+                    hugr.remove_subtree(func);
+                }
+            }
+        }
+        Ok(())
+    }
+}
+
+fn cycles<'a, N: Copy>(
+    g: impl Copy
+    + Visitable
+    + DataMap<NodeWeight = StaticNode<N>>
+    + IntoNeighbors
+    + IntoNodeIdentifiers
+    + NodeIndexable
+    + 'a,
+) -> impl Iterator<Item = Vec<N>> + 'a {
+    tarjan_scc(g)
+        .into_iter()
+        .filter(move |ns| {
+            ns.iter()
+                .exactly_one()
+                .ok()
+                .is_none_or(|n| // multi-node, or single-node cycle
+            g.neighbors(*n).contains(n))
+        })
+        .map(move |cycle| {
+            cycle
+                .into_iter()
+                .map(|n| match g.node_weight(n).unwrap() {
+                    StaticNode::FuncDefn(fd) => *fd,
+                    _ => panic!("Expected only FuncDefns in sccs"),
+                })
+                .collect()
+        })
+}
+
+fn do_inline<H: HugrMut>(call: H::Node, hugr: &mut H) {
+    match InlineCall::new(call).apply(hugr) {
+        Ok(()) => (),
+        Err(InlineCallError::NotCallNode(_, _) | InlineCallError::CallTargetNotFuncDefn(_, _)) => {
+            unreachable!();
+        }
+        Err(e) => {
+            todo!("Update to handle {e:?}")
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use rstest::rstest;
+    use std::collections::HashSet;
+
+    use hugr::{
+        HugrView,
+        builder::{
+            Container, Dataflow, DataflowHugr, DataflowSubContainer, FunctionBuilder, HugrBuilder,
+        },
+        extension::prelude::{qb_t, usize_t},
+        hugr::hugrmut::HugrMut,
+        ops::handle::NodeHandle,
+        types::Signature,
+    };
+    use hugr_passes::{ComposablePass, RemoveDeadFuncsPass, inline_dfgs::InlineDFGsPass};
+
+    use super::{InlineAnnotation, InlineError, InlinePass};
+
+    #[test]
+    fn test_single_cycle() {
+        let mut main = FunctionBuilder::new("main", Signature::new_endo([qb_t(), qb_t()])).unwrap();
+        let mut mb = main.module_root_builder();
+        let mut fb = mb
+            .define_function("self-call", Signature::new_endo([qb_t()]))
+            .unwrap();
+        let c = fb
+            .call::<true>(&fb.container_node().into(), &[], fb.input_wires())
+            .unwrap();
+        let fb = fb.finish_with_outputs(c.outputs()).unwrap();
+        let inputs = main.input_wires();
+        let mut hugr = main.finish_hugr_with_outputs(inputs).unwrap();
+        hugr.set_metadata::<InlineAnnotation>(fb.node(), InlineAnnotation::Always);
+        let backup = hugr.clone();
+
+        // We error even though the function is not called
+        let e = InlinePass::default().run(&mut hugr).unwrap_err();
+        assert_eq!(e, InlineError::AlwaysCycle(vec![fb.node()]));
+        assert_eq!(hugr, backup);
+
+        RemoveDeadFuncsPass::default().run(&mut hugr).unwrap();
+        assert_eq!(
+            hugr.children(hugr.module_root()).collect::<Vec<_>>(),
+            [hugr.entrypoint()]
+        );
+        let backup = hugr.clone();
+        InlinePass::default().run(&mut hugr).unwrap();
+        assert_eq!(hugr, backup);
+    }
+
+    #[test]
+    fn cycle() {
+        let mut main = FunctionBuilder::new("main", Signature::new_endo([usize_t()])).unwrap();
+        let main_h = main.container_node().into();
+        let mut mb = main.module_root_builder();
+        let mut fb1 = mb
+            .define_function("f1", Signature::new_endo([usize_t()]))
+            .unwrap();
+        let c1 = fb1.call::<true>(&main_h, &[], fb1.input_wires()).unwrap();
+        let fb1 = fb1.finish_with_outputs(c1.outputs()).unwrap();
+        let c2 = main.call(fb1.handle(), &[], main.input_wires()).unwrap();
+        let mut hugr = main.finish_hugr_with_outputs(c2.outputs()).unwrap();
+        hugr.set_metadata::<InlineAnnotation>(hugr.entrypoint(), InlineAnnotation::Always);
+        InlinePass::default().run(&mut hugr.clone()).unwrap(); // Ok
+
+        hugr.set_metadata::<InlineAnnotation>(fb1.node(), InlineAnnotation::Always);
+        let e = InlinePass::default().run(&mut hugr).unwrap_err();
+        assert_eq!(
+            e,
+            InlineError::AlwaysCycle(vec![fb1.node(), hugr.entrypoint()])
+        );
+    }
+
+    #[rstest]
+    fn test_one_deep(#[values(1, 2, 5)] num_calls: usize, #[values(false, true)] always: bool) {
+        let mut main =
+            FunctionBuilder::new("main", Signature::new_endo([qb_t(), qb_t(), qb_t()])).unwrap();
+
+        let mut mb = main.module_root_builder();
+        let swap = mb
+            .define_function("called-once", Signature::new_endo([qb_t(), qb_t()]))
+            .unwrap();
+        let [a, b] = swap.input_wires_arr();
+        let swap = swap.finish_with_outputs([b, a]).unwrap();
+
+        let [mut a, mut b, c] = main.input_wires_arr();
+        for _ in 0..num_calls {
+            [a, b] = main.call(swap.handle(), &[], [a, b]).unwrap().outputs_arr();
+        }
+        let mut hugr = main.finish_hugr_with_outputs([a, b, c]).unwrap();
+        if always {
+            hugr.set_metadata::<InlineAnnotation>(swap.node(), InlineAnnotation::Always);
+        }
+        let backup = hugr.clone();
+
+        InlinePass::default().run(&mut hugr).unwrap();
+        hugr.validate().unwrap();
+        let should_be_inlined = always || num_calls == 1;
+        if should_be_inlined {
+            let swap_present =
+                hugr.contains_node(swap.node()) && hugr.get_optype(swap.node()).is_func_defn();
+            assert!(!swap_present);
+            InlineDFGsPass::default().run(&mut hugr).unwrap();
+            hugr.validate().unwrap();
+            let [inp, outp] = hugr.get_io(hugr.entrypoint()).unwrap();
+            assert_eq!(
+                HashSet::from_iter(hugr.input_neighbours(outp)),
+                HashSet::from([inp])
+            );
+        } else {
+            assert_eq!(hugr, backup);
+        }
+    }
+
+    #[test]
+    fn entrypoint_scope() {
+        // TODO
+    }
+
+    // TODO cycle of one always func and one not always, should be inlined to a self-recursive func
+
+    // TODO cycle of two funcs where one has no other calls (and one has, or is preserved),
+    // should be inlined to a self-recursive func
+}