  Because calibrated light curves of Type Ia supernovae have become a major
tool to determine the local expansion rate of the Universe and also its
geometrical structure, considerable attention has been given to models of these
events over the past couple of years. There are good reasons to believe that
perhaps most Type Ia supernovae are the explosions of white dwarfs that have
approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by
thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such
accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent
progress in modeling Type Ia supernovae as well as several of the still open
questions are addressed in this review. Although the main emphasis will be on
studies of the explosion mechanism itself and on the related physical
processes, including the physics of turbulent nuclear combustion in degenerate
stars, we also discuss observational constraints.
