Appears in collection : Mostow rigidity and the marked length spectrum

We give an outline of Sullivan's proof of Mostow rigidity theorem for closed hyperbolic manifolds, using the notions of Patterson-Sullivan measures for discrete groups acting on CAT(-1) spaces, and the Bowen-Margulis measure, or the measure of maximal entropy for the geodesic flow of a closed negatively curved manifold. We also describe how these ideas lead to an equivalence between the following objects for a closed manifold of variable negative curvature: the marked length spectrum, the geodesic flow, and the cross-ratio on the boundary of the universal cover.