As mass is accreted on a White Dwarf (WD) in a mass-transferring binary, the inner layers are compressed and energy is released. The escape of this energy from the surface provides a floor to the WD surface temperature that can be observed directly during pauses in accretion. Released in the deep layers of the envelope, this energy also reheats the WD core, in effect resetting the cooling clock of the WD. We describe briefly how energy is released in the accreted envelope and core. The energy released by compression under accretion leads to an equilibrium core temperature, the key understanding the fate of all accreting WDs from progenitors of supernovae type Ia to the oldest low accretion rate systems. Both approach and departure from this equilibrium are important in relating the evolution of the WD to that of the binary. Consistent calculations of accreting WD thermal structure have led to new constraints on accretion rates in cataclysmic variables, have enabled classical novae observations to constrain the binary population, and have shed new light on the variety of classical novae. Evolutionary calculations have opened new avenues for discovery of the oldest CV systems, and have confirmed an evolutionary picture for AM CVn (double WD helium accreting) systems. Theoretical WD structures based on this work provide the essential basis for seismological studies of CV primaries which show non-radial oscillations.