  Core-collapse supernovae are among Nature's grandest explosions. They are
powered by the energy released in gravitational collapse and include a rich set
of physical phenomena involving all fundamental forces and many branches of
physics and astrophysics. We summarize the current state of core-collapse
supernova theory and discuss the current set of candidate explosion mechanisms
under scrutiny as core-collapse supernova modeling is moving towards
self-consistent three-dimensional simulations. Recent work in nuclear theory
and neutron star mass and radius measurements are providing new constraints for
the nuclear equation of state. We discuss these new developments and their
impact on core-collapse supernova modeling. Neutrino-neutrino forward
scattering in the central regions of core-collapse supernovae can lead to
collective neutrino flavor oscillations that result in swaps of electron and
heavy-lepton neutrino spectra. We review the rapid progress that is being made
in understanding these collective oscillations and their potential impact on
the core-collapse supernova explosion mechanism.
