In this seminar I will first describe the frontiers of our knowledge on neutrino flavor evolution in dense media - core-collapse supernovae, binary neutron star mergers, early universe. Indeed this constitutes a complex many-body problem, as I will explain, where, in the last fifteen years, we have uncovered a variety of novel phenomena and made major progress. I will also mention connections of neutrino flavor evolution in dense media to other domains, in particular quantum information theory. How neutrinos change flavor, in astrophysical and cosmological environments, is tightly linked to known neutrino properties such as the neutrino mixings, and to key unknowns. In this respect I will consider the case of non-radiative neutrino decay and discuss its importance for future observations, in particular in relation with the diffuse supernova neutrino background, whose discovery might be imminent.
