Core-collapse supernovae, the violent deaths of massive stars, are among the most spectacular phenomena in astrophysics: Supernovae can only outshine their host galaxy for weeks; they are laboratories for the behavior of matter at extreme densities; and they also play a central role for the chemical evolution of galaxies, e.g. as the dominant producers of oxygen and many other elements. Yet the mechanism by which massive stars explode has eluded us for decades. As I shall explain in this talk, this is about to change: Recent first-principle 3D simulations of these events have finally been able to demonstrate that the most popular explosion scenario, the so-called neutrino-driven mechanism, is viable. Including the initial seed asymmetries in the progenitors from convective shell burning could further help to produce even more robust supernova explosion models. Distilling the physical essence of modern 3D supernova simulations into semi-analytic models also allows us to predict the properties of supernova explosions and compact remnants across the whole range of stellar initial masses in reasonable agreement with observations.