Core-Collapse Supernovae: Modeling between Pragmatism and Perfectionism

We briefly summarize recent efforts in Garching for modeling stellar core collapse and post-bounce evolution in one and two dimensions. The transport of neutrinos of all flavors is treated by iteratively solving the coupled system of frequency-dependent moment equations together with a model Boltzmann equation which provides the closure. A variety of progenitor stars, different nuclear equations of state, stellar rotation, and global asymmetries due to large-mode hydrodynamic instabilities have been investigated to ascertain the road to finally successful, convectively supported neutrino-driven explosions.