Small perturbations imposed on an integrable system cause a slow evolution. In the process of this evolution the system may pass through a state of a resonance. The phenomenon of capture into resonance consists in the system starting to evolve in such a way as to preserve the resonance property once it has arisen. The class of perturbations for this phenomenon to occur includes both non-Hamiltonian perturbations and slow change of parameters of Hamiltonian systems. In the talk, a general theory of passages through resonances and captures into resonance, as well as several examples of these phenomena in problems of charged particles acceleration, will be presented.