Abstract
A review of the various theoretical efforts to study the energy loss of ions in matter is presented. The first part of the paper, mainly of a tutorial character, deals with classical scattering theory and some fundamental concepts useful for further study. In the second part, the main theories for high-energy and low-energy electronic stopping are reviewed and then the difficulties in describing intermediate-energy stopping are discussed. Finally, the various approaches (empirical, semi-empirical, semi-phenomenological and first principles) that have led to satisfactory descriptions of the energy loss for the whole (non-relativistic) energy range are considered.