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.
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