Appears in collection : Colloque Scientifique International Poincaré 100

The cut locus of a complete Riemannian manifold goes back to the "Lignes de partage" which have been defined by Poincaré in his celebrated 1905 paper "Sur les lignes géodésiques des surfaces convexes". Given a point P on a (complete) Riemannian manifold, the cut locus from P is defined as the closure of the set of points which can be joined to P with at least two minimizing geodesics. The purpose of this talk is to review some of the results which have been obtained since the Poincaré paper concerning the structure, the size, or the curvature of the cut locus.