The problem of massive neutrino motion in the presence of
the background matter and external fields is reviewed.
The following subjects are discussed:  neutrino motion and
oscillations in matter and electromagnetic or gravitational fields;
neutrino electromagnetic properties, including the magnetic
moment and induced electric charge in matter and external
fields; neutrinos from neutron beta-decay in magnetized matter;
neutrino decay in matter and external electromagnetic fields;
the spin light of neutrino (SL/nu) in different background
environments (in particular, the SL/nu in matter and/or
magnetic and gravitational fields). The phenomenological
consequences of the discussed items for different
astrophysical and cosmology settings are also reviewed.