Computation and a wealth of new observational techniques have reinvigorated dynamical studies of galaxies and star clusters. These objects are examples of the gravitational n-body problem with n in the range from a few hundred to 1011. Relaxation effects dominate at the low end and are completely negligible at the high end. The gravitational n-body problem is chaotic, and the principal challenge in doing physics where that problem is involved (whether computationally or with analytic theory) is to ensure that chaos has not vitiated the results. Enforcing a Liouville theorem accomplishes this with collision-free large-n problems, but equivalent recipes are not in common use for smaller n. We describe some important insights and discoveries that have come from computation in stellar dynamics, discuss chaos briefly, and indicate the way the physics that comes up in different astronomical contexts is addressed in numerical methods currently in use. Graphics is a vital part of any computational approach. The long range prospects are very promising for continued high scientific productivity in stellar dynamics.