Rapid progress has been made during recent years in the understanding of the flavour oscillations that occur as neutrinos traverse through supernova. The previous paradigm has given way and it is now clear that the neutrino signals we shall receive from future galactic supernovae will allow us both to peer inside these extraordinary cosmic events and to probe some of the fundamental properties of these elusive particles. In this review, we aim to distill the progress that has been made focusing upon the effects of the dynamic density profile and the emergence of collective flavour oscillations due to neutrino self-interactions.