A rational mapping f : Ck − −− > Ck is said to be birational if it has a rational inverse. We will discuss some aspects of the dynamics of birational maps. In particular, we address the question of how to determine the dynamical degree, which is the growth rate of degree (f n) with respect to n. We give some examples of mappings where it is possible to determine the dynamical degree by studying the action of f n on the cohomology group H1,1 These examples exhibit behaviors that do not occur in dimension 2. This is joint work with Jeff Diller and with Kyounghee Kim.