diff --git a/mvpoly/README.md b/mvpoly/README.md
index 7f4fa0d862..447e56811f 100644
--- a/mvpoly/README.md
+++ b/mvpoly/README.md
@@ -1,4 +1,4 @@
-## MVPoly: symbolic interpreter of multivariate polynomials
+# MVPoly: play with multi-variate poynomials
 
 This library aims to provide algorithms and different representations to
 manipulate multivariate polynomials.
diff --git a/mvpoly/src/lib.rs b/mvpoly/src/lib.rs
index 054efbda28..a54f61186b 100644
--- a/mvpoly/src/lib.rs
+++ b/mvpoly/src/lib.rs
@@ -1,3 +1,15 @@
+//! This module contains the definition of the `MVPoly` trait, which is used to
+//! represent multi-variate polynomials.
+//!
+//! Different representations are provided in the sub-modules:
+//! - `monomials`: a representation based on monomials
+//! - `prime`: a representation based on a mapping from variables to prime
+//! numbers. This representation is unmaintained for now. We leave it
+//! for interested users.
+//!
+//! "Expressions", as defined in the [kimchi] crate, can be converted into a
+//! multi-variate polynomial using the `from_expr` method.
+
 use std::collections::HashMap;
 
 use ark_ff::PrimeField;