The cosmic gamma-ray background radiation is one of the most fundamental observables in
the gamma-ray band. Although the origin of the cosmic gamma-ray background radiation has
been a mystery for a long time, the Fermi gamma-ray space telescope has recently
measured it at 0.1-820 GeV and revealed that the cosmic GeV gamma-ray background is
composed of blazars, radio galaxies, and star-forming galaxies. However, Fermi still
leaves the following questions. Those are dark matter contribution, origins of the
cosmic MeV gamma-ray background, and the connection to the IceCube TeV-PeV neutrino
events. In this talk, I will review the current understandings of the cosmic gamma-ray
background and discuss future prospects of cosmic gamma-ray background radiation
studies.