N-body models are now a standard tool to improve our understanding of galaxies. Since photometric and kinematic observations of a galaxy do not in general very strongly constrain a dynamical model, the main use of N-body simulations in this respect is to answer qualitative questions about the nature of possible equilibria. This is illustrated by presenting a model with strong radial ellipticity gradients and one with intrinsic principal axes twists. Another important application of N-body methods is in the study of transient phenomena.