Neutrino flavor evolution in dense neutrino media such as those expected in core-collapse supernovae and neutron star merger remnants is a very rich and nonlinear phenomenon. Indeed the neutrino-neutrino interaction is so strong that it can lead to collective oscillations of the whole neutrino gas. Collective neutrino oscillations can play an important role in the physics of core-collapse supernovae and neutron star merger remnants. In this seminar I will describe this interesting phenomenon and I will explain why and how this phenomenon modifies the 
physics of such environments. I will then talk about some recent development and the current status of the field. I will finally discuss an intriguing phenomenon in which neutrino-neutrino interactions can significantly modify the flavor ratio of a class of high energy astrophysical neutrinos."