Many modern accelerators can produce high-velocity beams of complex nuclei. They are true “atom-smashers,” capable of causing dramatic nuclear reactions. This chapter explores how collisions of nuclei with increasing velocities lead to increasingly excited states of nuclear matter. It presents concepts of macroscopic physics to describe phenomena like phase transitions and hydrodynamic flow. The microscopic theory of heavy-ion reactions has not yet progressed far enough to provide a detailed description of all the very complicated observations. Nevertheless, a reasonably coherent picture has emerged which enables us to begin to study nuclear matter under extreme conditions somewhat like those in a collapsing supernova or in the early universe. The main reaction process for collisions near the grazing angular momentum is the transfer of nucleons between target and projectile. The best theoretical method for treating the memories stored in the motion of the individual nucleons during large changes of the mean field is the time-dependent mean field theory or Time-Dependent IIartree-Fock.