Compact binary systems, consisting of a neutron star/black hole as one of the binary stars, are ideal for studying energetic physics near compact objects. The recent development of gamma-ray
observations enabled the study of high-energy emission features in some compact binary systems, and it revealed their nature as cosmic-ray accelerators in the Galaxy. In this talk, I review our
observations of the gamma-ray binary systems, a subclass of high-mass X-ray binaries, showing non-thermal emissions above 1 MeV. We performed multiwavelength/timing analysis using Fermi, Suzaku, NuSTAR, and NICER and studied its efficient electron acceleration and the nature of the compact binary behind it. I also want to discuss the prospects of future observations, mainly focusing on the upcoming MeV gamma-ray satellite COSI, including the strategy of its data analysis.