  We present quite a powerful method in investigations of different phenomena
that can appear when neutrinos and electrons propagate in background matter.
This method implies use of exact solutions of modified Dirac equations that
contain the correspondent effective potentials accounting for the matter
influence on particles. For several particular cases the exact solutions of
modified Dirac and Dirac-Pauli equations for a neutrino and an electron in the
background environment of different composition are obtained (the case of
magnetized matter is also considered). Neutrino reflection, trapping, neutrino
pair creation and annihilation in matter and neutrino energy quantization in a
rotating medium are discussed. The neutrino Green functions in matter are also
derived. The two recently proposed mechanisms of electromagnetic radiation by a
neutrino and an electron in matter (the spin light of neutrino and electron,
$SL\nu$ and $SLe$) are considered. A possibility to introduce an effective
"matter-induced Lorentz force" acting on a neutrino and an electron is
discussed. A new mechanism of electromagnetic radiation that can be emitted by
an electron moving in the neutrino background with non-zero gradient of density
is predicted.
