  We briefly review some equilibrium and nonequilibrium properties of systems
with long-range interactions. Such systems, which are characterized by a
potential that weakly decays at large distances, have striking properties at
equilibrium, like negative specific heat in the microcanonical ensemble,
temperature jumps at first order phase transitions, broken ergodicity. Here, we
mainly restrict our analysis to mean-field models, where particles globally
interact with the same strength. We show that relaxation to equilibrium
proceeds through quasi-stationary states whose duration increases with system
size. We propose a theoretical explanation, based on Lynden-Bell's entropy, of
this intriguing relaxation process. This allows to address problems related to
nonequilibrium using an extension of standard equilibrium statistical
mechanics. We discuss in some detail the example of the dynamics of the free
electron laser, where the existence and features of quasi-stationary states is
likely to be tested experimentally in the future. We conclude with some
perspectives to study open problems and to find applications of these ideas to
dipolar media.
