In spite of its simple crystal structure, the electronic properties of the iron-based superconductor FeSe (Tc ~ 9 K) is rich and attractive. Superconductivity in FeSe takes place in a so-called nematic phase that is associated with orbital ordering. Another interesting aspect is that Fermi wave length is as long as the coherence length; FeSe is most likely in the BCS-BEC crossover regime. We have performed spectroscopic-imaging STM experiments on FeSe to investigate its electronic structures. There are two superconducting gaps in the spectrum; the larger one (~ 2.5 meV) is on the hole band at the Brillouin-zone center and the smaller one (~ 1.2 meV) is on the electron band at the zone corner. Multiband superconductivity aspects, symmetry of the order parameter, role of disorder, vortex matter and chemical substitution effects on the band structure of this system will be discussed.