Thurston's Ending Lamination Conjecture provides a conjectural classification of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold $M$. This classification is in terms of topological data, the marked homeomorphism type of the manifold, and geometric data, which encodes the asymptotic geometry of the ends of the manifold. Brock, Canary and Minsky recently established this conjecture in the case when $M$ has incompressible boundary. We will discuss the conjecture and some consequences of its proof.