  Core-collapse supernovae are among the most energetic cosmic cataclysms. They
are prodigious emitters of neutrinos and quite likely strong galactic sources
of gravitational waves. Observation of both neutrinos and gravitational waves
from the next galactic or near extragalactic core-collapse supernova will yield
a wealth of information on the explosion mechanism, but also on the structure
and angular momentum of the progenitor star, and on aspects of fundamental
physics such as the equation of state of nuclear matter at high densities and
low entropies. In this contribution to the proceedings of the Neutrino 2012
conference, we summarize recent progress made in the theoretical understanding
and modeling of core-collapse supernovae. In this, our emphasis is on
multi-dimensional processes involved in the explosion mechanism such as
neutrino-driven convection and the standing accretion shock instability. As an
example of how supernova neutrinos can be used to probe fundamental physics, we
discuss how the rise time of the electron antineutrino flux observed in
detectors can be used to probe the neutrino mass hierarchy. Finally, we lay out
aspects of the neutrino and gravitational-wave signature of core-collapse
supernovae and discuss the power of combined analysis of neutrino and
gravitational wave data from the next galactic core-collapse supernova.
