diff --git a/Cargo.lock b/Cargo.lock
index 1f15047cb..4ad454e80 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -3813,7 +3813,6 @@ dependencies = [
  "json-depth-checker",
  "levenshtein_automata",
  "liquid",
- "log",
  "logging_timer",
  "maplit",
  "md5",
diff --git a/milli/Cargo.toml b/milli/Cargo.toml
index 10ad2fb8f..4bc05d2cc 100644
--- a/milli/Cargo.toml
+++ b/milli/Cargo.toml
@@ -71,7 +71,6 @@ itertools = "0.11.0"
 puffin = "0.16.0"
 
 # logging
-log = "0.4.20"
 logging_timer = "1.1.0"
 csv = "1.3.0"
 candle-core = { git = "https://github.com/huggingface/candle.git", version = "0.3.1" }
diff --git a/milli/src/search/mod.rs b/milli/src/search/mod.rs
index 7bac5ea0c..e411bd032 100644
--- a/milli/src/search/mod.rs
+++ b/milli/src/search/mod.rs
@@ -6,9 +6,9 @@ use charabia::Normalize;
 use fst::automaton::{Automaton, Str};
 use fst::{IntoStreamer, Streamer};
 use levenshtein_automata::{LevenshteinAutomatonBuilder as LevBuilder, DFA};
-use log::error;
 use once_cell::sync::Lazy;
 use roaring::bitmap::RoaringBitmap;
+use tracing::error;
 
 pub use self::facet::{FacetDistribution, Filter, OrderBy, DEFAULT_VALUES_PER_FACET};
 pub use self::new::matches::{FormatOptions, MatchBounds, MatcherBuilder, MatchingWords};
diff --git a/milli/src/search/new/bucket_sort.rs b/milli/src/search/new/bucket_sort.rs
index b439b87ec..e7bafaf70 100644
--- a/milli/src/search/new/bucket_sort.rs
+++ b/milli/src/search/new/bucket_sort.rs
@@ -166,6 +166,9 @@ pub fn bucket_sort<'ctx, Q: RankingRuleQueryTrait>(
             continue;
         }
 
+        let span = tracing::trace_span!(target: "search::bucket_sort", "next_bucket", id = ranking_rules[cur_ranking_rule_index].id());
+        let entered = span.enter();
+
         let Some(next_bucket) = ranking_rules[cur_ranking_rule_index].next_bucket(
             ctx,
             logger,
@@ -175,6 +178,7 @@ pub fn bucket_sort<'ctx, Q: RankingRuleQueryTrait>(
             back!();
             continue;
         };
+        drop(entered);
 
         ranking_rule_scores.push(next_bucket.score);
 
diff --git a/milli/src/update/facet/mod.rs b/milli/src/update/facet/mod.rs
index ad8a838c8..400507c97 100644
--- a/milli/src/update/facet/mod.rs
+++ b/milli/src/update/facet/mod.rs
@@ -85,8 +85,8 @@ use charabia::normalizer::{Normalize, NormalizerOption};
 use grenad::{CompressionType, SortAlgorithm};
 use heed::types::{Bytes, DecodeIgnore, SerdeJson};
 use heed::BytesEncode;
-use log::debug;
 use time::OffsetDateTime;
+use tracing::debug;
 
 use self::incremental::FacetsUpdateIncremental;
 use super::FacetsUpdateBulk;
diff --git a/milli/src/update/index_documents/enrich.rs b/milli/src/update/index_documents/enrich.rs
index 82ea335ae..162136912 100644
--- a/milli/src/update/index_documents/enrich.rs
+++ b/milli/src/update/index_documents/enrich.rs
@@ -78,7 +78,7 @@ pub fn enrich_documents_batch<R: Read + Seek>(
                 },
                 [] => return Ok(Err(UserError::NoPrimaryKeyCandidateFound)),
                 [(field_id, name)] => {
-                    log::info!("Primary key was not specified in index. Inferred to '{name}'");
+                    tracing::info!("Primary key was not specified in index. Inferred to '{name}'");
                     PrimaryKey::Flat { name, field_id: *field_id }
                 }
                 multiple => {
diff --git a/milli/src/update/index_documents/extract/extract_fid_docid_facet_values.rs b/milli/src/update/index_documents/extract/extract_fid_docid_facet_values.rs
index 2449e01cd..1f8af372d 100644
--- a/milli/src/update/index_documents/extract/extract_fid_docid_facet_values.rs
+++ b/milli/src/update/index_documents/extract/extract_fid_docid_facet_values.rs
@@ -431,7 +431,7 @@ fn extract_facet_values(value: &Value, geo_field: bool) -> FilterableValues {
                     if let Ok(float) = original.parse() {
                         output_numbers.push(float);
                     } else {
-                        log::warn!(
+                        tracing::warn!(
                             "Internal error, could not parse a geofield that has been validated. Please open an issue."
                         )
                     }
diff --git a/milli/src/update/index_documents/extract/extract_vector_points.rs b/milli/src/update/index_documents/extract/extract_vector_points.rs
index 0bf7333e3..117f6cc8c 100644
--- a/milli/src/update/index_documents/extract/extract_vector_points.rs
+++ b/milli/src/update/index_documents/extract/extract_vector_points.rs
@@ -186,12 +186,12 @@ pub fn extract_vector_points<R: io::Read + io::Seek>(
                         prompt.render(obkv, DelAdd::Deletion, field_id_map).unwrap_or_default();
                     let new_prompt = prompt.render(obkv, DelAdd::Addition, field_id_map)?;
                     if old_prompt != new_prompt {
-                        log::trace!(
+                        tracing::trace!(
                             "🚀 Changing prompt from\n{old_prompt}\n===to===\n{new_prompt}"
                         );
                         VectorStateDelta::NowGenerated(new_prompt)
                     } else {
-                        log::trace!("⏭️ Prompt unmodified, skipping");
+                        tracing::trace!("⏭️ Prompt unmodified, skipping");
                         VectorStateDelta::NoChange
                     }
                 } else {
diff --git a/milli/src/update/index_documents/extract/mod.rs b/milli/src/update/index_documents/extract/mod.rs
index f0fd97965..357cdf8d7 100644
--- a/milli/src/update/index_documents/extract/mod.rs
+++ b/milli/src/update/index_documents/extract/mod.rs
@@ -14,8 +14,8 @@ use std::fs::File;
 use std::io::BufReader;
 
 use crossbeam_channel::Sender;
-use log::debug;
 use rayon::prelude::*;
+use tracing::debug;
 
 use self::extract_docid_word_positions::extract_docid_word_positions;
 use self::extract_facet_number_docids::extract_facet_number_docids;
diff --git a/milli/src/update/index_documents/mod.rs b/milli/src/update/index_documents/mod.rs
index cbcde19fc..ca3d6bdd1 100644
--- a/milli/src/update/index_documents/mod.rs
+++ b/milli/src/update/index_documents/mod.rs
@@ -13,11 +13,11 @@ use std::result::Result as StdResult;
 use crossbeam_channel::{Receiver, Sender};
 use heed::types::Str;
 use heed::Database;
-use log::debug;
 use rand::SeedableRng;
 use roaring::RoaringBitmap;
 use serde::{Deserialize, Serialize};
 use slice_group_by::GroupBy;
+use tracing::debug;
 use typed_chunk::{write_typed_chunk_into_index, TypedChunk};
 
 use self::enrich::enrich_documents_batch;
diff --git a/milli/src/update/index_documents/typed_chunk.rs b/milli/src/update/index_documents/typed_chunk.rs
index 7db0279ba..37399dcd5 100644
--- a/milli/src/update/index_documents/typed_chunk.rs
+++ b/milli/src/update/index_documents/typed_chunk.rs
@@ -517,7 +517,7 @@ pub(crate) fn write_typed_chunk_into_index(
                 }
             }
 
-            log::debug!("Finished vector chunk for {}", embedder_name);
+            tracing::debug!("Finished vector chunk for {}", embedder_name);
         }
         TypedChunk::ScriptLanguageDocids(sl_map) => {
             let span = tracing::trace_span!(target: "indexing::write_db", "script_language_docids");
diff --git a/milli/src/update/words_prefix_integer_docids.rs b/milli/src/update/words_prefix_integer_docids.rs
index 23a676bc8..a05eb8721 100644
--- a/milli/src/update/words_prefix_integer_docids.rs
+++ b/milli/src/update/words_prefix_integer_docids.rs
@@ -4,7 +4,7 @@ use std::str;
 use grenad::CompressionType;
 use heed::types::Bytes;
 use heed::{BytesDecode, BytesEncode, Database};
-use log::debug;
+use tracing::debug;
 
 use crate::error::SerializationError;
 use crate::heed_codec::StrBEU16Codec;
diff --git a/milli/src/vector/hf.rs b/milli/src/vector/hf.rs
index cdfdbfb75..04e169c71 100644
--- a/milli/src/vector/hf.rs
+++ b/milli/src/vector/hf.rs
@@ -73,7 +73,7 @@ impl Embedder {
         let device = match candle_core::Device::cuda_if_available(0) {
             Ok(device) => device,
             Err(error) => {
-                log::warn!("could not initialize CUDA device for Hugging Face embedder, defaulting to CPU: {}", error);
+                tracing::warn!("could not initialize CUDA device for Hugging Face embedder, defaulting to CPU: {}", error);
                 candle_core::Device::Cpu
             }
         };
diff --git a/milli/src/vector/openai.rs b/milli/src/vector/openai.rs
index 104decb66..cbddddfb7 100644
--- a/milli/src/vector/openai.rs
+++ b/milli/src/vector/openai.rs
@@ -173,12 +173,16 @@ impl Embedder {
             let retry_duration = match result {
                 Ok(embeddings) => return Ok(embeddings),
                 Err(retry) => {
-                    log::warn!("Failed: {}", retry.error);
+                    tracing::warn!("Failed: {}", retry.error);
                     tokenized |= retry.must_tokenize();
                     retry.into_duration(attempt)
                 }
             }?;
-            log::warn!("Attempt #{}, retrying after {}ms.", attempt, retry_duration.as_millis());
+            tracing::warn!(
+                "Attempt #{}, retrying after {}ms.",
+                attempt,
+                retry_duration.as_millis()
+            );
             tokio::time::sleep(retry_duration).await;
         }
 
@@ -244,7 +248,7 @@ impl Embedder {
                         .map_err(EmbedError::openai_unexpected)
                         .map_err(Retry::retry_later)?;
 
-                    log::warn!("OpenAI: input was too long, retrying on tokenized version. For best performance, limit the size of your prompt.");
+                    tracing::warn!("OpenAI: input was too long, retrying on tokenized version. For best performance, limit the size of your prompt.");
 
                     return Err(Retry::retry_tokenized(EmbedError::openai_too_many_tokens(
                         error_response.error,
@@ -266,7 +270,7 @@ impl Embedder {
         client: &reqwest::Client,
     ) -> Result<Vec<Embeddings<f32>>, Retry> {
         for text in texts {
-            log::trace!("Received prompt: {}", text.as_ref())
+            tracing::trace!("Received prompt: {}", text.as_ref())
         }
         let request = OpenAiRequest {
             model: self.options.embedding_model.name(),
@@ -289,7 +293,7 @@ impl Embedder {
             .map_err(EmbedError::openai_unexpected)
             .map_err(Retry::retry_later)?;
 
-        log::trace!("response: {:?}", response.data);
+        tracing::trace!("response: {:?}", response.data);
 
         Ok(response
             .data