During a period of about two decades we have realized a programme of systematic investigations of different aspects of neutrino propagation in extreme external environments and have predicted and studied several new phenomena that are engendered by the presence of external magnetic fields and dense matter.
The starting point that underlies the research is the fact that the electromagnetic properties of neutrinos open a window to new physics \cite{Giunti:2014ixa,Studenikin:2008bd, Studenikin:2018vnp}. In these brief notes, we recall several new phenomena that have been proposed and investigated earlier. In particular, we discuss:
1) the spin light of neutrino in matter, 2) the neutrino energy quantization in rotating matter, and 3) neutrino start turning mechanism. Then we dwell on results of recent studies:
4) the effects of interplay of neutrino flavour and spin oscillations in a magnetic field, 5) the quantum theory of neutrino spin and spin-flavour oscillations engendered by the transversal mater currents, 6) the amplitude modulation of the flavour neutrino oscillation probability by the transversal matter current. As for references to the literature, only those papers are included in which a particular effect was proposed and considered for the first time and in a number of cases references are also be given to the most recent articles, which contain detailed references to the available literature on the issue.