  The FeSe superconductor and its related systems have attracted much attention
in the iron-based superconductors owing to their simple crystal structure and
peculiar electronic and physical properties. The bulk FeSe superconductor has a
superconducting transition temperature (Tc) of ~8 K; it can be dramatically
enhanced to 37 K at high pressure. On the other hand, its cousin system, FeTe,
possesses a unique antiferromagnetic ground state but is non-superconducting.
Substitution of Se by Te in the FeSe superconductor results in an enhancement
of Tc up to 14.5 K and superconductivity can persist over a large composition
range in the Fe(Se,Te) system. Intercalation of the FeSe superconductor leads
to the discovery of the AxFe2-ySe2 (A=K, Cs and Tl) system that exhibits a Tc
higher than 30 K and a unique electronic structure of the superconducting
phase. The latest report of possible high temperature superconductivity in the
single-layer FeSe/SrTiO3 films with a Tc above 65 K has generated much
excitement in the community. This pioneering work opens a door for interface
superconductivity to explore for high Tc superconductors. The distinct
electronic structure and superconducting gap, layer-dependent behavior and
insulator-superconductor transition of the FeSe/SrTiO3 films provide critical
information in understanding the superconductivity mechanism of the iron-based
superconductors. In this paper, we present a brief review on the investigation
of the electronic structure and superconductivity of the FeSe superconductor
and related systems, with a particular focus on the FeSe films.
