The study of heavy ion collisions is motivated by the desire to probe properties of nuclear matter under unusual. conditions. Depending on the energy of the beam and the impact parameter of the collision, different phenomena are observed. A survey of typical experimental data and their interpretations are presented. For heavy ion collisions at low energies, the reaction is dominated by irreversible, non-equilibrium processes. Both the time-dependent mean-field theory and the statistical tranport theory are employed for understanding these reactions. At high energies, the main part of heavy ion reactions is due to the multiple scatterings between the projectile nucleons and the target nucleons. We discuss both the linear cascade model and the statistical model.