  Supernova theory, numerical and analytic, has made remarkable progress in the
past decade. This progress was made possible by more sophisticated simulation
tools, especially for neutrino transport, improved microphysics, and deeper
insights into the role of hydrodynamic instabilities. Violent, large-scale
nonradial mass motions are generic in supernova cores. The neutrino-heating
mechanism, aided by nonradial flows, drives explosions, albeit low-energy ones,
of ONeMg-core and some Fe-core progenitors. The characteristics of the neutrino
emission from new-born neutron stars were revised, new features of the
gravitational-wave signals were discovered, our notion of supernova
nucleosynthesis was shattered, and our understanding of pulsar kicks and
explosion asymmetries was significantly improved. But simulations also suggest
that neutrino-powered explosions might not explain the most energetic
supernovae and hypernovae, which seem to demand magnetorotational driving. Now
that modeling is being advanced from two to three dimensions, more realism, new
perspectives, and hopefully answers to long-standing questions are coming into
reach.
