Well known theorems of Mostov and Prasad assert that the fundamental group determines the geometry of a finite volume 3-dimensional hyperbolic manifold. Some years ago, Thurston suggested the following generalization: The geometry of any 3-dimensional hyperbolic manifold with finitely generated fundamental group is determined by this group and a finite collection of "end invariants". The end invariants come in two flavours: They are either Teichmüller parameters (for geometrically finite ends) or laminations (for simply degenerate ends). We will give an introduction to this topic and indicate how, recently, Y. Minsky and his collaborators have managed to prove this assertion of Thurston, known as the Ending Lamination Conjecture.