  We highlight the progress in our understanding of how neutrinos change their
flavor in astrophysical environments, in particular effects from the neutrino
self-interaction. We emphasize extended descriptions of neutrino propagation in
massive stars that are beyond the current one based on the mean-field
approximation. The extended equations include, in particular, corrections from
(anti)neutrino-(anti)neutrino pairing correlations and from the neutrino mass.
We underline open issues and challenges.
