diff --git a/milli/src/search/criteria/mod.rs b/milli/src/search/criteria/mod.rs
index 34d06dce3..41cd6722c 100644
--- a/milli/src/search/criteria/mod.rs
+++ b/milli/src/search/criteria/mod.rs
@@ -10,6 +10,7 @@ use super::query_tree::{Operation, Query, QueryKind};
 pub mod typo;
 pub mod words;
 pub mod asc_desc;
+pub mod proximity;
 
 pub trait Criterion {
     fn next(&mut self) -> anyhow::Result<Option<CriterionResult>>;
diff --git a/milli/src/search/criteria/proximity.rs b/milli/src/search/criteria/proximity.rs
new file mode 100644
index 000000000..2a46cf5d0
--- /dev/null
+++ b/milli/src/search/criteria/proximity.rs
@@ -0,0 +1,283 @@
+use std::collections::HashMap;
+use std::mem::take;
+
+use roaring::RoaringBitmap;
+
+use crate::search::query_tree::{maximum_proximity, Operation, Query};
+use super::{Candidates, Criterion, CriterionResult, Context, query_docids, query_pair_proximity_docids};
+
+pub struct Proximity<'t> {
+    ctx: &'t dyn Context,
+    query_tree: Option<(usize, Operation)>,
+    proximity: u8,
+    candidates: Candidates,
+    bucket_candidates: Option<RoaringBitmap>,
+    parent: Option<Box<dyn Criterion + 't>>,
+    candidates_cache: HashMap<(Operation, u8), Vec<(Query, Query, RoaringBitmap)>>,
+}
+
+impl<'t> Proximity<'t> {
+    pub fn initial(
+        ctx: &'t dyn Context,
+        query_tree: Option<Operation>,
+        candidates: Option<RoaringBitmap>,
+    ) -> anyhow::Result<Self> where Self: Sized
+    {
+        Ok(Proximity {
+            ctx,
+            query_tree: query_tree.map(|op| (maximum_proximity(&op), op)),
+            proximity: 0,
+            candidates: candidates.map_or_else(Candidates::default, Candidates::Allowed),
+            bucket_candidates: None,
+            parent: None,
+            candidates_cache: HashMap::new(),
+        })
+    }
+
+    pub fn new(
+        ctx: &'t dyn Context,
+        parent: Box<dyn Criterion + 't>,
+    ) -> anyhow::Result<Self> where Self: Sized
+    {
+        Ok(Proximity {
+            ctx,
+            query_tree: None,
+            proximity: 0,
+            candidates: Candidates::default(),
+            bucket_candidates: None,
+            parent: Some(parent),
+            candidates_cache: HashMap::new(),
+        })
+    }
+}
+
+impl<'t> Criterion for Proximity<'t> {
+    fn next(&mut self) -> anyhow::Result<Option<CriterionResult>> {
+        use Candidates::{Allowed, Forbidden};
+        loop {
+            match (&mut self.query_tree, &mut self.candidates) {
+                (_, Allowed(candidates)) if candidates.is_empty() => {
+                    self.query_tree = None;
+                    self.candidates = Candidates::default();
+                },
+                (Some((max_prox, query_tree)), Allowed(candidates)) => {
+                    if self.proximity as usize > *max_prox {
+                        self.query_tree = None;
+                        self.candidates = Candidates::default();
+                    } else {
+                        let mut new_candidates = resolve_candidates(
+                            self.ctx,
+                            &query_tree,
+                            self.proximity,
+                            &mut self.candidates_cache,
+                        )?;
+
+                        new_candidates.intersect_with(&candidates);
+                        candidates.difference_with(&new_candidates);
+                        self.proximity += 1;
+
+                        let bucket_candidates = match self.parent {
+                            Some(_) => self.bucket_candidates.take(),
+                            None => Some(new_candidates.clone()),
+                        };
+
+                        return Ok(Some(CriterionResult {
+                            query_tree: Some(query_tree.clone()),
+                            candidates: new_candidates,
+                            bucket_candidates,
+                        }));
+                    }
+                },
+                (Some((max_prox, query_tree)), Forbidden(candidates)) => {
+                    if self.proximity as usize > *max_prox {
+                        self.query_tree = None;
+                        self.candidates = Candidates::default();
+                    } else {
+                        let mut new_candidates = resolve_candidates(
+                            self.ctx,
+                            &query_tree,
+                            self.proximity,
+                            &mut self.candidates_cache,
+                        )?;
+
+                        new_candidates.difference_with(&candidates);
+                        candidates.union_with(&new_candidates);
+                        self.proximity += 1;
+
+                        let bucket_candidates = match self.parent {
+                            Some(_) => self.bucket_candidates.take(),
+                            None => Some(new_candidates.clone()),
+                        };
+
+                        return Ok(Some(CriterionResult {
+                            query_tree: Some(query_tree.clone()),
+                            candidates: new_candidates,
+                            bucket_candidates,
+                        }));
+                    }
+                },
+                (None, Allowed(_)) => {
+                    let candidates = take(&mut self.candidates).into_inner();
+                    return Ok(Some(CriterionResult {
+                        query_tree: None,
+                        candidates: candidates.clone(),
+                        bucket_candidates: Some(candidates),
+                    }));
+                },
+                (None, Forbidden(_)) => {
+                    match self.parent.as_mut() {
+                        Some(parent) => {
+                            match parent.next()? {
+                                Some(CriterionResult { query_tree, candidates, bucket_candidates }) => {
+                                    self.query_tree = query_tree.map(|op| (maximum_proximity(&op), op));
+                                    self.proximity = 0;
+                                    self.candidates = Candidates::Allowed(candidates);
+                                    self.bucket_candidates = bucket_candidates;
+                                },
+                                None => return Ok(None),
+                            }
+                        },
+                        None => return Ok(None),
+                    }
+                },
+            }
+        }
+    }
+}
+
+fn resolve_candidates<'t>(
+    ctx: &'t dyn Context,
+    query_tree: &Operation,
+    proximity: u8,
+    cache: &mut HashMap<(Operation, u8), Vec<(Query, Query, RoaringBitmap)>>,
+) -> anyhow::Result<RoaringBitmap>
+{
+    fn resolve_operation<'t>(
+        ctx: &'t dyn Context,
+        query_tree: &Operation,
+        proximity: u8,
+        cache: &mut HashMap<(Operation, u8), Vec<(Query, Query, RoaringBitmap)>>,
+    ) -> anyhow::Result<Vec<(Query, Query, RoaringBitmap)>>
+    {
+        use Operation::{And, Consecutive, Or, Query};
+
+        let result = match query_tree {
+            And(ops) => mdfs(ctx, ops, proximity, cache)?,
+            Consecutive(ops) => if proximity == 0 {
+                mdfs(ctx, ops, 0, cache)?
+            } else {
+                Default::default()
+            },
+            Or(_, ops) => {
+                let mut output = Vec::new();
+                for op in ops {
+                    let result = resolve_operation(ctx, op, proximity, cache)?;
+                    output.extend(result);
+                }
+                output
+            },
+            Query(q) => if proximity == 0 {
+                let candidates = query_docids(ctx, q)?;
+                vec![(q.clone(), q.clone(), candidates)]
+            } else {
+                Default::default()
+            },
+        };
+
+        Ok(result)
+    }
+
+    fn mdfs_pair<'t>(
+        ctx: &'t dyn Context,
+        left: &Operation,
+        right: &Operation,
+        proximity: u8,
+        cache: &mut HashMap<(Operation, u8), Vec<(Query, Query, RoaringBitmap)>>,
+    ) -> anyhow::Result<Vec<(Query, Query, RoaringBitmap)>>
+    {
+        fn pair_combinations(mana: u8) -> impl Iterator<Item = (u8, u8)> {
+            (0..=mana).map(move |m| (mana - m, m))
+        }
+
+        let mut output = Vec::new();
+
+        for (pair_p, left_right_p) in pair_combinations(proximity) {
+            for (left_p, right_p) in pair_combinations(left_right_p) {
+                let left_key = (left.clone(), left_p);
+                if !cache.contains_key(&left_key) {
+                    let candidates = resolve_operation(ctx, left, left_p, cache)?;
+                    cache.insert(left_key.clone(), candidates);
+                }
+
+                let right_key = (right.clone(), right_p);
+                if !cache.contains_key(&right_key) {
+                    let candidates = resolve_operation(ctx, right, right_p, cache)?;
+                    cache.insert(right_key.clone(), candidates);
+                }
+
+                let lefts = cache.get(&left_key).unwrap();
+                let rights = cache.get(&right_key).unwrap();
+
+                for (ll, lr, lcandidates) in lefts {
+                    for (rl, rr, rcandidates) in rights {
+                        let mut candidates = query_pair_proximity_docids(ctx, lr, rl, pair_p + 1)?;
+                        if lcandidates.len() < rcandidates.len() {
+                            candidates.intersect_with(lcandidates);
+                            candidates.intersect_with(rcandidates);
+                        } else {
+                            candidates.intersect_with(rcandidates);
+                            candidates.intersect_with(lcandidates);
+                        }
+                        if !candidates.is_empty() {
+                            output.push((ll.clone(), rr.clone(), candidates));
+                        }
+                    }
+                }
+            }
+        }
+
+        Ok(output)
+    }
+
+    fn mdfs<'t>(
+        ctx: &'t dyn Context,
+        branches: &[Operation],
+        proximity: u8,
+        cache: &mut HashMap<(Operation, u8), Vec<(Query, Query, RoaringBitmap)>>,
+    ) -> anyhow::Result<Vec<(Query, Query, RoaringBitmap)>>
+    {
+        // Extract the first two elements but gives the tail
+        // that is just after the first element.
+        let next = branches.split_first().map(|(h1, t)| {
+            (h1, t.split_first().map(|(h2, _)| (h2, t)))
+        });
+
+        match next {
+            Some((head1, Some((head2, [_])))) => mdfs_pair(ctx, head1, head2, proximity, cache),
+            Some((head1, Some((head2, tail)))) => {
+                let mut output = Vec::new();
+                for p in 0..=proximity {
+                    for (lhead, _, head_candidates) in mdfs_pair(ctx, head1, head2, p, cache)? {
+                        if !head_candidates.is_empty() {
+                            for (_, rtail, mut candidates) in mdfs(ctx, tail, proximity - p, cache)? {
+                                candidates.intersect_with(&head_candidates);
+                                if !candidates.is_empty() {
+                                    output.push((lhead.clone(), rtail, candidates));
+                                }
+                            }
+                        }
+                    }
+                }
+                Ok(output)
+            },
+            Some((head1, None)) => resolve_operation(ctx, head1, proximity, cache),
+            None => return Ok(Default::default()),
+        }
+    }
+
+    let mut candidates = RoaringBitmap::new();
+    for (_, _, cds) in resolve_operation(ctx, query_tree, proximity, cache)? {
+        candidates.union_with(&cds);
+    }
+    Ok(candidates)
+}
diff --git a/milli/src/search/mod.rs b/milli/src/search/mod.rs
index 51f81f540..aced8bbd1 100644
--- a/milli/src/search/mod.rs
+++ b/milli/src/search/mod.rs
@@ -11,7 +11,7 @@ use once_cell::sync::Lazy;
 use roaring::bitmap::RoaringBitmap;
 
 use crate::search::criteria::{Criterion, CriterionResult};
-use crate::search::criteria::{typo::Typo, words::Words, asc_desc::AscDesc};
+use crate::search::criteria::{typo::Typo, words::Words, proximity::Proximity};
 use crate::{Index, DocumentId};
 
 pub use self::facet::{FacetCondition, FacetDistribution, FacetNumberOperator, FacetStringOperator};
@@ -87,17 +87,19 @@ impl<'a> Search<'a> {
 
         debug!("facet candidates: {:?} took {:.02?}", facet_candidates, before.elapsed());
 
-        // We aretesting the typo criteria but there will be more of them soon.
+        // We are testing the typo criteria but there will be more of them soon.
         let criteria_ctx = criteria::HeedContext::new(self.rtxn, self.index)?;
         let typo_criterion = Typo::initial(&criteria_ctx, query_tree, facet_candidates)?;
         let words_criterion = Words::new(&criteria_ctx, Box::new(typo_criterion))?;
+        let proximity_criterion = Proximity::new(&criteria_ctx, Box::new(words_criterion))?;
+        // let proximity_criterion = Proximity::initial(&criteria_ctx, query_tree, facet_candidates)?;
+        let mut criteria = proximity_criterion;
 
-        // We sort in descending order on a specific field *by hand*, don't do that at home.
-        let attr_name = "released-timestamp";
-        let fid = self.index.fields_ids_map(self.rtxn)?.id(attr_name).unwrap();
-        let ftype = *self.index.faceted_fields(self.rtxn)?.get(attr_name).unwrap();
-        let desc_criterion = AscDesc::desc(self.index, self.rtxn, Box::new(words_criterion), fid, ftype)?;
-        let mut criteria = desc_criterion;
+        // // We sort in descending order on a specific field *by hand*, don't do that at home.
+        // let attr_name = "released-timestamp";
+        // let fid = self.index.fields_ids_map(self.rtxn)?.id(attr_name).unwrap();
+        // let ftype = *self.index.faceted_fields(self.rtxn)?.get(attr_name).unwrap();
+        // let desc_criterion = AscDesc::desc(self.index, self.rtxn, Box::new(words_criterion), fid, ftype)?;
 
         let mut offset = self.offset;
         let mut limit = self.limit;
diff --git a/milli/src/search/query_tree.rs b/milli/src/search/query_tree.rs
index 715a4864e..59f7802f3 100644
--- a/milli/src/search/query_tree.rs
+++ b/milli/src/search/query_tree.rs
@@ -79,6 +79,13 @@ impl Operation {
             Self::Consecutive(ops)
         }
     }
+
+    pub fn query(&self) -> Option<&Query> {
+        match self {
+            Operation::Query(query) => Some(query),
+            _ => None,
+        }
+    }
 }
 
 #[derive(Clone, Eq, PartialEq, Hash)]