From fundamental principles, the interaction of directed energetic electrons with hydrogenic and arbitrary-Z plasmas is analytically modeled. The effects of stopping, straggling, and beam blooming, a consequence of scattering and energy loss, are rigorously treated from a unified approach. Enhanced energy deposition occurs in the latter portion of the penetration and is inextricably linked to straggling and blooming. These effects, which have a strong Z dependence, will be important in evaluating the requirements of fast ignition and tolerable levels of electron preheat.