Core-collapse supernovae are among Natures 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.
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