  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.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena