  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
proceeding, I will review the current understandings of the cosmic gamma-ray
background and discuss future prospects of cosmic gamma-ray background
radiation studies. I also briefly review the current status of cosmic
infrared/optical background radiation studies.
