Neutrino flavor evolution in a dense neutrino medium, such as the one anticipated in the supernova environment, is a very rich and nonlinear phenomenon which has not been understood well.
In this talk, I will first discuss why understanding neutrino
flavor oscillations is crucial to the comprehension of the supernova physics. I will then talk about some of the recent developments in the field. In particular, I will discuss the neutrino evolution in multidimensional models and the occurrence of the so-called fast modes in the supernova environment.