Matter effects in the theory of neutrino propagation in a medium are reviewed. The quasi-classical (which is based on the generalized Bargmann-Michel-Tellegdi equation for the neutrino spin) and quantum (based on the generalized Dirac equation for the neutrino wave function) approaches to the neutrino spin evolution and oscillations in matter are discussed. On this basis the quasi-classical and quantum theories of the new type of the electromagnetic radiation by a neutrino in matter - neutrino-spin light (SL?) - is developed.

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