  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 $\omega$, dc supercurrent, and
inelastic relaxation rates, assuming that the microwave power is weak enough
and can be treated perturbatively. In the phase diagram ($\omega,T$) the region
of superconductivity enhancement occupies a finite area located near $T_c$. At
sufficiently high frequencies and low temperatures, the effect of direct
depairing prevails over quasiparticle redistribution, always leading to
superconductivity suppression.
