It has been shown by Bonahon, Agol, Calegari and Gabai that a complete hyperbolic 3-manifold with finitely generated fundamental group is topologically finite. This was conjectured by Marden, and via a geometric reinterpretation by Thurston, has become known as the ``Tameness Theorem''. In this paper we give an account of this result, inspired by arguments of Soma, which is as far as possible self-contained. We also describe how it can be generalised to pinched negative curvature, and how it implies a version of Ahlfors's finiteness theorem in this context.
Enseign. Math. 56 (2010) 229-285.