Publisher Summary This chapter presents the recent developments in a single collection, representing the state of the art in energy deposition theory. It focuses on various methods and approaches for calculating the stopping cross-section or properties, as well as the various terms in the series expansion of the stopping cross-section. The quantity is velocity dependent, and carries a negative sign so that the stopping power would be positive as the projectile slows. As simple energy and momentum conservation demand, at all but the lowest projectile velocities, the stopping power comes from collisions of the projectile with target electrons, and thus from energy transfer to the electronic structure of the target atoms, molecules, or solid. The stopping power is generally normalized by the target scatterer density n, to produce the stopping cross-section, S (v).