Twenty years after SN 1987A, the vast international programme of experimental neutrino physics and astronomy guarantees that large detectors will observe a high-statistics neutrino signal from a galactic SN. In this context, I will talk about possible signatures in the observable neutrino signal, associated to neutrino flavor oscillations in supernovae. In particular, I will discuss about the surprising new effects on SN neutrino oscillations, associated to the neutrino self-interactions near a supernova core.