  Nova explosions occur on the white dwarf component of a Cataclysmic Variable
binary stellar system that is accreting matter lost by its companion. When
sufficient material has been accreted by the white dwarf, a thermonuclear
runaway occurs and ejects material in what is observed as a Classical Nova
explosion. We describe both the recent advances in our understanding of the
progress of the outburst and outline some of the puzzles that are still
outstanding. We report on the effects of improving both the nuclear reaction
rate library and including a modern nuclear reaction network in our
one-dimensional, fully implicit, hydrodynamic computer code. In addition, there
has been progress in observational studies of Supernovae Ia with implications
about the progenitors and we discuss that in this review.
