Neutrinos play a crucial role in the collapse and explosion of massive stars, governing the infall dynamics of the stellar core, triggering and fueling the explosion and driving the cooling and deleptonization of the newly formed neutron star. Due to their role neutrinos carry information from the heart of the explosion and, due to their weakly interacting nature, offer the only direct probe of the dynamics and thermodynamics at the center of a supernova. In this paper, we review the present status of modelling the neutrino physics and signal formation in collapsing and exploding stars. We assess the capability of current and planned large underground neutrino detectors to yield faithful information of the time and flavor dependent neutrino signal from a future Galactic supernova. We show how the observable neutrino burst would provide a benchmark for fundamental supernova physics with unprecedented richness of detail. Exploiting the treasure of the measured neutrino events requires a careful discrimination of source-generated properties from signal features that originate on the way to the detector. As for the latter, we discuss self-induced flavor
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