All of the technologies described here fundamentally derive from the interactions of energetic electrons with matter; that is, scattering processes, the creation and emission of secondary electrons, and processes by which the kinetic energy of an incident electron is absorbed into materials. These mechanisms are statistical processes that can be described by cross-sections. We use these crosssections in a variety of Monte Carlo simulations to study the spatial distributions of energy deposition and stochastic emission processes in crystalline and amorphous “hard” materials, soft materials such as molecular, polymeric, and liquid systems, and gaseous species.