In his 1966 ICM address, Smale proposed a program to understand Anosov flows, a class of hyperbolic dynamical systems. This program has been particularly fruitful in dimension 3. In this talk, we give an outline of a proof that there are only finitely many Anosov and pseudo-Anosov flows up to orbit equivalence on a hyperbolic 3-manifold. This is joint work with David Gabai.