We review a variety of theoretical and experimental results concerning electronic band structure of superconducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems AxFe2Se2-xSx and [Li1-xFexOH]FeSe as well as the single FeSe layer films on SrTiO3 substrate. We present the results of detailed first principle electronic band structure calculations for these systems together with comparison with some experimental ARPES data. The electronic structure of these systems is rather different from that of typical FeAs superconductors, which is quite significant for possible microscopic mechanism of superconductivity. This is reflected in the absence of hole pockets of the Fermi surface at T-point in Brillouin zone, so that there are no "nesting" properties of different Fermi surface pockets. LDA + DMFT calculations show that correlation effects on Fe-3d states in the single FeSe layer are not that strong as in most of FeAs systems. As a result, at present there is no theoretical understanding of the formation of rather "shallow" electronic bands at M-points. LDA calculations show that the main difference in electronic structure of FeSe monolayer on SrTiO3 substrate from isolated FeSe layer is the presence of the band of O-2p surface states of TiO2 layer on the Fermi level together with Fe-3d states, which may be important for understanding the enhanced Tc values in this system. We briefly discuss the implications of our results for microscopic models of superconductivity.