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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.
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