  This review discusses the main experiments and theoretical views related to observation of high-temperature superconductivity in intercalated FeSe compounds and single layer films of FeSe on substrates like SrTiO_3. We consider in detail the electronic structure of these systems, both theoretical calculations of this structure at hand and their correspondence with ARPES experiments. It is stressed that electronic spectrum of these systems is qualitatively different from typical picture of the spectrum in well studied FeAs superconductors and the related problems of theoretical description of spectrum formation are also discussed. We also discuss the possible mechanisms of Cooper pairing in monolayers of FeSe and problems appearing here. As single layer films of FeSe on SrTiO_3 can be represented as typical Ginzburg "sandwiches", we analyze the possibility of rising the critical temperature of superconducting transition T_c due to different variants of "excitonic" mechanism of superconductivity. It is shown, that in its classic variant (as proposed for such systems by Allender, Bray and Bardeen) this mechanism is unable to explain the observed values of T_c, but situation is different when we consider instead of "excitons" the optical phonons in SrTiO_3 (with energy of the order of 100 meV). We consider both the simplest model of T_c enhancement due to interaction with such phonons and more specific models with dominant "forward" scattering, which allow to understand the growth of T_c as compared with the case of bulk FeSe and intercalated FeSe systems. We also discuss the problems connected with antiadiabatic nature of superconductivity due to such mechanism. 
High Temperature Superconductivity in FeSe Monolayers