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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
We bring to light a novel mechanism through which turbulent matter density fluctuations can induce collective neutrino flavor
Neutrino oscillations in the Earth matter may introduce peculiar modulations in the supernova (SN) neutrino spectra. The detection of this effect has been proposed as diagnostic tool for the neutrino mass hierarchy at large 1-3 leptonic mixing angle
The spatial and velocity distributions of nuclear species synthesized in the innermost regions of core-collapse supernovae can yield important clues about explosion asymmetries and the operation of the still disputed explosion mechanism. Recent obser
Core-collapse supernovae emit of order $10^{58}$ neutrinos and antineutrinos of all flavors over several seconds, with average energies of 10--25 MeV. In the Sudbury Neutrino Observatory (SNO), a future Galactic supernova at a distance of 10 kpc woul
Tidal disruption events are an excellent probe for supermassive black holes in distant inactive galaxies because they show bright multi-wavelength flares lasting several months to years. AT2019dsg presents the first potential association with neutrino emission from such an explosive event.