For ten years, the Boltzmann equation (with some modifications to take
into account some quantum effects) has been the basis of models for t
he description of heavy ion reactions; these models have the common fe
ature that they simulate the Boltzmann equation (under various names a
s: Landau-Vlasov, Boltzmann-Uehling-Uhlenbeck, Boltzmann-Nordheim...)
rather than they solve it explicitly. This report presents the basic n
umerical principles of the Boltzmann models in Heavy Ion Physics and t
heir links with other modelizations of the N-Body Problem used in othe
r fields of Physics. It discusses their validity and some applications
arbitrarily chosen among the most relevant ones.