I will give a general overview of the astrophysical circumstances which may lead to the catastrophic incineration of a white dwarf (WD) star by thermonuclear burning. The proposed scenarios under which an explosion can occur will be contrasted with those in which a collapse is expected. However, these two remarkably different outcomes share many of the same physical processes, an understanding of which is required for accurate simulation of either. The efficient numerical equation of state (EOS) which is used in large-scale multi-dimensional simulations of WD incineration will be discussed explicitly. After reviewing the important physical EOS contributions, I will discuss in detail how the plasma Coulomb corrections in the EOS are related to the charge screening of nuclear reactions. This relationship will then find immediate application in a consistent framework for determination of the nuclear statistical equilibrium (NSE) state of the burned material in the WD in the presence of reaction screening. Finally I will discuss the impact of dynamic adjustment of the NSE state on the thermodynamic and therefore hydrodynamic properties of the WD matter, particularly regarding the buoyancy of burned material, and how this plays out during the deflagration stage of a supernova.