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The problem of non-linearity of luminescence is reviewed on the basis of kinetic equations for concentrations and two-particle correlation functions. The reasons of time dependence of the rates of reactions between excitations are discussed. The non-linearity of luminescence and non-exponentiality of its decay is attributed to initial correlation between excitations created by photons, and to non-homogeneous spatial distribution of deposited energy. The case of excitation by ionizing particle is discussed. The equation for the scintillation yield and decay kinetics with account for either small energy losses (plasmons, excitons and electron-hole pairs) or large energy losses (delta-electrons and Auger cascade) is obtained.