  The term ``violent relaxation'' was coined by Donald Lynden-Bell as a
memorable oxymoron describing how a stellar dynamical system relaxes from a
chaotic initial state to a quasi-equilibrium. His analysis showed that this
process is rapid, even for systems with many stars, and that it leads to
equilibria which may plausibly be related to bounded isothermal spheres. I
review how numerical simulations have improved our understanding of violent
relaxation over the last thirty years. It is clear that the process leads to
equilibria which depend strongly on the initial state, but which nevertheless
have certain common features. A particularly interesting case concerns objects
formed in an expanding universe through dissipationless hierarchical clustering
from gaussian initial conditions; these may correspond to galaxy clusters or to
the dark halos of galaxies. While such objects display a wide range of shapes
and spins, the distributions of these properties depend only weakly on the
cosmological context and on the initial spectrum of density fluctuations. Halo
density profiles appear to have a universal form with a singular central
structure and a characteristic density which depends only on formation epoch.
Low mass halos typically have earlier formation times and thus higher
characteristic densities than high mass halos.
