  We discuss the recent progress in our understanding of neutrino flavour
conversion in core-collapse supernovae and focus on the effects coming from the
neutrino-neutrino interaction. The latter has been shown to engender new
phenomena, modifying significantly the neutrino fluxes and supernova
observations. In particular, we make the link between the spectral split and
the magnetic resonance phenomenon. Moreover, recent investigations have
demonstrated the existence of leptonic CP violation effects on the supernova
neutrino fluxes. We summarize these findings.
