Despite 80 years of research, the mechanism of core- collapse supernova explosions and the precise nucleosynthesis of supernovae in general, still hold significant and exciting mysteries for the field of nuclear-astrophysics. What is the central ignition density for the white-dwarf model of the Type Ia supernova? What is the energy spectrum of neutrinos trapped during the collapse and post-bounce evolution of a massive core-collapse supernova? How can simulation reproduce the observed light curves and atomic spectra of these events? Are the explosion mechanisms robust or chaotic...