3D core-collapse supernova modeling and applications to Cas A and other supernova remnants

First three-dimensional, first-principle simulations of core-collapse supernovae have become possible in the recent past. They demonstrate the basic viability of the neutrino-driven mechanism for powering the explosions of the majority of supernova progenitors. Although a number of open questions remain to be settled, the explosion models are now sufficiently mature to strive for detailed comparisons against observations, for example considering well studied, nearby supernovae and young supernova remnants. This talk will review our basic understanding of the explosion mechanism and report some results of such observational tests.