diff --git a/src/convergence.rs b/src/convergence.rs
new file mode 100644
index 0000000..d03359c
--- /dev/null
+++ b/src/convergence.rs
@@ -0,0 +1,31 @@
+//! Convergence configuration and reporting.
+
+use std::time::Duration;
+
+use smallvec::SmallVec;
+
+#[derive(Clone, Copy, Debug)]
+pub struct ConvergenceOptions {
+    pub max_iter: usize,
+    pub epsilon: f64,
+}
+
+impl Default for ConvergenceOptions {
+    fn default() -> Self {
+        Self {
+            max_iter: crate::ITERATIONS,
+            epsilon: crate::EPSILON,
+        }
+    }
+}
+
+/// Post-hoc summary of a `History::converge` call.
+#[derive(Clone, Debug)]
+pub struct ConvergenceReport {
+    pub iterations: usize,
+    pub final_step: (f64, f64),
+    pub log_evidence: f64,
+    pub converged: bool,
+    pub per_iteration_time: SmallVec<[Duration; 32]>,
+    pub slices_skipped: usize,
+}
diff --git a/src/history.rs b/src/history.rs
index f162b3c..8545d8d 100644
--- a/src/history.rs
+++ b/src/history.rs
@@ -3,8 +3,11 @@ use std::collections::HashMap;
 use crate::{
     BETA, GAMMA, Index, MU, N_INF, P_DRAW, SIGMA,
     competitor::{self, Competitor},
+    convergence::{ConvergenceOptions, ConvergenceReport},
     drift::{ConstantDrift, Drift},
+    error::InferenceError,
     gaussian::Gaussian,
+    observer::{NullObserver, Observer},
     rating::Rating,
     sort_time,
     storage::CompetitorStore,
@@ -14,17 +17,20 @@ use crate::{
 };
 
 #[derive(Clone)]
-pub struct HistoryBuilder<T: Time = i64, D: Drift<T> = ConstantDrift> {
+pub struct HistoryBuilder<T: Time = i64, D: Drift<T> = ConstantDrift, O: Observer<T> = NullObserver>
+{
     mu: f64,
     sigma: f64,
     beta: f64,
     drift: D,
     p_draw: f64,
     online: bool,
+    convergence: ConvergenceOptions,
+    observer: O,
     _time: std::marker::PhantomData<T>,
 }
 
-impl<T: Time, D: Drift<T>> HistoryBuilder<T, D> {
+impl<T: Time, D: Drift<T>, O: Observer<T>> HistoryBuilder<T, D, O> {
     pub fn mu(mut self, mu: f64) -> Self {
         self.mu = mu;
         self
@@ -40,7 +46,7 @@ impl<T: Time, D: Drift<T>> HistoryBuilder<T, D> {
         self
     }
 
-    pub fn drift<D2: Drift<T>>(self, drift: D2) -> HistoryBuilder<T, D2> {
+    pub fn drift<D2: Drift<T>>(self, drift: D2) -> HistoryBuilder<T, D2, O> {
         HistoryBuilder {
             drift,
             mu: self.mu,
@@ -48,7 +54,9 @@ impl<T: Time, D: Drift<T>> HistoryBuilder<T, D> {
             beta: self.beta,
             p_draw: self.p_draw,
             online: self.online,
-            _time: std::marker::PhantomData,
+            convergence: self.convergence,
+            observer: self.observer,
+            _time: self._time,
         }
     }
 
@@ -62,7 +70,26 @@ impl<T: Time, D: Drift<T>> HistoryBuilder<T, D> {
         self
     }
 
-    pub fn build(self) -> History<T, D> {
+    pub fn convergence(mut self, opts: ConvergenceOptions) -> Self {
+        self.convergence = opts;
+        self
+    }
+
+    pub fn observer<O2: Observer<T>>(self, observer: O2) -> HistoryBuilder<T, D, O2> {
+        HistoryBuilder {
+            mu: self.mu,
+            sigma: self.sigma,
+            beta: self.beta,
+            drift: self.drift,
+            p_draw: self.p_draw,
+            online: self.online,
+            convergence: self.convergence,
+            observer,
+            _time: self._time,
+        }
+    }
+
+    pub fn build(self) -> History<T, D, O> {
         History {
             size: 0,
             time_slices: Vec::new(),
@@ -73,18 +100,20 @@ impl<T: Time, D: Drift<T>> HistoryBuilder<T, D> {
             drift: self.drift,
             p_draw: self.p_draw,
             online: self.online,
+            convergence: self.convergence,
+            observer: self.observer,
         }
     }
 }
 
-impl HistoryBuilder<i64, ConstantDrift> {
+impl<O: Observer<i64>> HistoryBuilder<i64, ConstantDrift, O> {
     pub fn gamma(mut self, gamma: f64) -> Self {
         self.drift = ConstantDrift(gamma);
         self
     }
 }
 
-impl Default for HistoryBuilder<i64, ConstantDrift> {
+impl Default for HistoryBuilder<i64, ConstantDrift, NullObserver> {
     fn default() -> Self {
         Self {
             mu: MU,
@@ -93,12 +122,14 @@ impl Default for HistoryBuilder<i64, ConstantDrift> {
             drift: ConstantDrift(GAMMA),
             p_draw: P_DRAW,
             online: false,
+            convergence: ConvergenceOptions::default(),
+            observer: NullObserver,
             _time: std::marker::PhantomData,
         }
     }
 }
 
-pub struct History<T: Time = i64, D: Drift<T> = ConstantDrift> {
+pub struct History<T: Time = i64, D: Drift<T> = ConstantDrift, O: Observer<T> = NullObserver> {
     size: usize,
     pub(crate) time_slices: Vec<TimeSlice<T>>,
     pub(crate) agents: CompetitorStore<T, D>,
@@ -108,31 +139,23 @@ pub struct History<T: Time = i64, D: Drift<T> = ConstantDrift> {
     drift: D,
     p_draw: f64,
     online: bool,
+    convergence: ConvergenceOptions,
+    observer: O,
 }
 
-impl Default for History<i64, ConstantDrift> {
+impl Default for History<i64, ConstantDrift, NullObserver> {
     fn default() -> Self {
-        Self {
-            size: 0,
-            time_slices: Vec::new(),
-            agents: CompetitorStore::new(),
-            mu: MU,
-            sigma: SIGMA,
-            beta: BETA,
-            drift: ConstantDrift(GAMMA),
-            p_draw: P_DRAW,
-            online: false,
-        }
+        HistoryBuilder::default().build()
     }
 }
 
-impl History<i64, ConstantDrift> {
-    pub fn builder() -> HistoryBuilder<i64, ConstantDrift> {
+impl History<i64, ConstantDrift, NullObserver> {
+    pub fn builder() -> HistoryBuilder<i64, ConstantDrift, NullObserver> {
         HistoryBuilder::default()
     }
 }
 
-impl<T: Time, D: Drift<T>> History<T, D> {
+impl<T: Time, D: Drift<T>, O: Observer<T>> History<T, D, O> {
     fn iteration(&mut self) -> (f64, f64) {
         let mut step = (0.0, 0.0);
 
@@ -243,9 +266,39 @@ impl<T: Time, D: Drift<T>> History<T, D> {
             .map(|ts| ts.log_evidence(self.online, targets, forward, &self.agents))
             .sum()
     }
+
+    /// Run the full forward+backward convergence loop and return a summary.
+    pub fn converge(&mut self) -> Result<ConvergenceReport, InferenceError> {
+        use std::time::Instant;
+
+        use smallvec::SmallVec;
+
+        let opts = self.convergence;
+        let mut step = (f64::INFINITY, f64::INFINITY);
+        let mut i = 0;
+        let mut per_iter: SmallVec<[std::time::Duration; 32]> = SmallVec::new();
+        while tuple_gt(step, opts.epsilon) && i < opts.max_iter {
+            let t0 = Instant::now();
+            step = self.iteration();
+            per_iter.push(t0.elapsed());
+            i += 1;
+            self.observer.on_iteration_end(i, step);
+        }
+        let converged = !tuple_gt(step, opts.epsilon);
+        let log_evidence = self.log_evidence(false, &[]);
+        self.observer.on_converged(i, step, converged);
+        Ok(ConvergenceReport {
+            iterations: i,
+            final_step: step,
+            log_evidence,
+            converged,
+            per_iteration_time: per_iter,
+            slices_skipped: 0,
+        })
+    }
 }
 
-impl<D: Drift<i64>> History<i64, D> {
+impl<D: Drift<i64>, O: Observer<i64>> History<i64, D, O> {
     pub fn add_events(
         &mut self,
         composition: Vec<Vec<Vec<Index>>>,
@@ -1287,4 +1340,39 @@ mod tests {
         assert_ulps_eq!(lc[&a][1].1, lc[&a][0].1, epsilon = 1e-6);
         assert_ulps_eq!(lc[&b][1].1, lc[&a][0].1, epsilon = 1e-6);
     }
+
+    #[test]
+    fn test_converge_returns_report() {
+        use crate::ConvergenceOptions;
+
+        let mut index_map = crate::KeyTable::new();
+        let a = index_map.get_or_create("a");
+        let b = index_map.get_or_create("b");
+        let c = index_map.get_or_create("c");
+        let composition = vec![
+            vec![vec![a], vec![b]],
+            vec![vec![a], vec![c]],
+            vec![vec![b], vec![c]],
+        ];
+        let results = vec![vec![1.0, 0.0], vec![0.0, 1.0], vec![1.0, 0.0]];
+        let times: Vec<i64> = vec![1, 2, 3];
+
+        let mut h = History::builder()
+            .mu(0.0)
+            .sigma(2.0)
+            .beta(1.0)
+            .drift(ConstantDrift(0.0))
+            .convergence(ConvergenceOptions {
+                max_iter: 30,
+                epsilon: 1e-6,
+            })
+            .build();
+        h.add_events(composition, results, times, vec![]);
+
+        let report = h.converge().unwrap();
+        assert!(report.converged);
+        assert!(report.iterations > 0);
+        assert!(report.iterations < 30);
+        assert!(report.final_step.0 <= 1e-6);
+    }
 }
diff --git a/src/lib.rs b/src/lib.rs
index d4efa2d..5a397fc 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -10,6 +10,7 @@ mod time;
 mod time_slice;
 pub use time_slice::TimeSlice;
 mod competitor;
+mod convergence;
 pub mod drift;
 mod error;
 mod event;
@@ -26,6 +27,7 @@ pub(crate) mod schedule;
 pub mod storage;
 
 pub use competitor::Competitor;
+pub use convergence::{ConvergenceOptions, ConvergenceReport};
 pub use drift::{ConstantDrift, Drift};
 pub use error::InferenceError;
 pub use event::{Event, Member, Team};