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.
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