Abstract: Stellar evolution is currently an exercise in spherical symmetry. The hydrodynamic processes taking place in stars, however, do not share this symmetry. Simplified models of the underlying hydrodynamics have been formulated, and have been quite successful in explaining the gross properties of stars. These models fail, however, when confronted with more stringent observational tests. The failures have given birth to simplistic prescriptions for additional mixing beyond the boundaries of convection zones dubbed "overshoot" and "penetration". These obfuscating notions need to be replaced with a more complete underlying physical picture. It is with this goal in mind that we have undertaken multi-dimensional hydrodynamic simulations of stellar interiors. Drawing upon the results of these calculations as well as laboratory and geophysical experiment and theory, we formulate an alternative description of how a convection zone couples to an adjacent stably stratified region within a stellar interior. Some implications for massive star evolution and supernova theory will be discussed.