What shall we learn from a future supernova?

Core-collapse supernovae constitute a unique laboratory for particle physics and astrophysics. They are powerful neutrino sources of all flavors, emitting essentially all the gravitational binding energy through neutrinos, at the end of their life. I will highlight how crucial is the observation of the next core-collapse supernova and of the diffuse supernova neutrino background, whose discovery might be imminent.