Effects related with deviations from thermodynamic equilibrium take a special place in the modern physics. Among those, non-equilibrium phenomena in quantum systems attract the highest interest. To date, the experimental technique of spin noise spectroscopy has became quite widespread, which makes possible to observe spin fluctuations of charge carriers in semiconductors both in equilibrium and non-equilibrium conditions. It calls for development of the theory of spin fluctuations of electrons and electron-hole complexes for non-equilibrium conditions. In this paper we consider a range of physical situations where a deviation from an equilibrium becomes pronounced in the spin noise. A general method of calculation of electron and exciton spin fluctuations in non-equilibrium state is proposed. A short review of theoretical and experimental results in this area is given.