2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121815In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the complex of curves and the geometry of Teichmueller space.17 pages, 2 figures; final version, to appear in "Handbook of Teichmueller theory"Geometric Topology30F60text