We review recent progress in the theory of electromagnetic response of dirty superconductors subject to microwave radiation. The theory originally developed by Eliashberg in 1970 and soon after that elaborated in a number of publications addressed the effect of superconductivity enhancement in the vicinity of the transition temperature. This effect originates from nonequilibrium redistribution of quasiparticles and requires a minimal microwave frequency depending on the inelastic relaxation rate and temperature. In a recent series of papers we generalized the Eliashberg theory to arbitrary temperatures T , microwave frequencies ω, dc supercurrent, and inelastic relaxation rates, assuming that the microwave power is weak enough and can be treated perturbatively. In the phase diagram (ω, T ) the region of superconductivity enhancement occupies a finite area located near Tc. At sufficiently high frequencies and low temperatures, the effect of direct depairing prevails over quasiparticle redistribution, always leading to superconductivity suppression. arXiv:1911.04959v1 [cond-mat.supr-con]