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It is well known that massive neutrinos have nontrivial electromagnetic properties, and at least the magnetic moment is not zero [1]. Thus, neutrinos do participate also in the electromagnetic interaction (see [2] for a review). The best terrestrial laboratory upper bound on neutrino magnetic moments is obtained by the GEMMA reactor neutrino experiment [3]. The best astrophysical upper bound was derived from considering stars cooling [4]. The neutrino magnetic moment procession in the transversal magnetic field B⊥ was first considered in [5], then spin-flavor precession in vacuum was discussed in [6], the importance of the matter effect was emphasized in [7]. The effect of resonant amplification of neutrino spin oscillations in B in the presence of matter was proposed in [8, 9], the impact of the longitudinal magnetic field B|| was discussed in [10]. Here below we discuss three very interesting aspects related to the neutrino spin and spin-flavour oscillations: 1) we consider in details neutrino mixing and oscillations in arbitrary constant magnetic field that have B⊥ and B|| nonzero components, 2) we show that neutrino spin and spin-flavour oscillations can be induced not only by the neutrino interaction with a magnetic field but also by neutrino interactions with matter in the case when there is a transversal matter current or matter polarization, 3) we develop a new (and more precise than the usual one) approach to description of neutrino spin and spin-flavor oscillations in the presence of an arbitrary magnetic field; our approach is based on the use of the stationary states in the magnetic field for classification of neutrino spin states, contrary to the customary approach based on the neutrino helicity states.