In this talk we report recent results obtained by the nuclear astrophysics group in Basel,
in modeling the collapse of the iron core of a massive star (M > 8 Solar masses). These
extreme events happen at the end of the stellar nuclear burning stages, ans result in the
explosion of the star and in the formation of a compact object at the center.
Properties of matter under extreme conditions of density and temperature, weak interaction
and neutrinos, as well as multidimensional magnetohydrodynamics play a key role in these stellar explosion, and have to be taken simultaneously into account in large computational models. After several decades of intense research, the actual mechanism that finally triggers the explosion is still uncertain and several different hypothesis have been proposed. The main focus of the presentation will be the discussion and the modeling of two of such possible explosion mechanisms: the neutrino-driven mechanism and the magneto-rotationally driven mechanism.