  The ${\it {spin \ \ light \ \ of \ \ neutrino}}$ ($SL\nu$) is a new possible
mechanism of electromagnetic radiation by a massive neutrino (with a nonzero
magnetic moment) moving in media. Since the prediction of this mechanism, the
question has been debated in a number of publications as whether the effect can
be of any significance for realistic astrophysical conditions. Although this
effect is strongly suppressed due to smallness of neutrino magnetic moment, for
ultra-high energy neutrinos (PeV neutrinos recently observed by the IceCube
collaboration, for instance) the $SL\nu$ might be of interest in the case of
neutrinos propagating in dense matter. An advanced view on the $SL\nu$ in
matter is given, and several astrophysical settings (a neutron star, supernova,
Gamma-Ray Burst (GRB), and relic neutrino background) for which the effect can
be realized are considered. Taking into account the threshold condition and
also several competing processes, we determine conditions for which the $SL\nu$
mechanism is possible. We conclude that the most favorable case of the effect
manifestation is provided by ultra dense matter of neutron stars and ultrahigh
energy of the radiating neutrino, and note that these conditions can be met
within galaxy clusters. It is also shown that due to the $SL\nu$ specific
polarization properties this electromagnetic mechanism is of interest in the
connection with the observed polarization of GRB emission.
