This review first discusses the different types of numerical methods available for integrating the equations of motion of N-body systems. It is desirable to supplement ordinary integration schemes with special treatments of close encounters using a two-body perturbation description or introducing regularizing transformations of the co-ordinates and time. Direct methods are at present limited to the study of a few hundred particles but larger systems may be investigated using Monte Carlo techniques or the Boltzmann moment equations.
N-body computations have been performed for a whole range of initial conditions and the general results are summarized. Numerical investigations have already clarified a number of important aspects of cluster evolution and the qualitative behaviour of small stellar systems is now quite well understood. Recent theoretical modifications have reduced the disagreement with experiments but further improvements are still needed.