Many explosive astrophysical events are powered by rapid thermonuclear burning, and the outcome of an event, the distribution and energy of nuclides in the remnant, depends sensitively on the details of this burning. Modeling astrophysical explosions presents a challenge because the disparity between the length scale of the star and that of thermonuclear flames can be 10-12 orders of magnitude. I will present an overview of thermonuclear flames and combustion and the effects of fluid instabilities and background turbulence. I will also describe efforts to capture the essence of sub-grid-scale burning in parameterized models and the development of post-processing routines used to obtain detailed composition by integrating density and temperature histories of Lagrangian tracer particles. Finally, I will present simulations of thermonuclear supernovae that combine these elements to explain observed trends in the brightness of events.