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We have a workable and testable hypothesis for the origin of the extragalactic gamma-ray background measured by EGRET, viz., that it is made up primarily of unresolved blazars. The GLAST gamma-ray telescope, to be flown in the near future, will be able to test this hypothesis in three ways, i.e., (a) by potentially resolving out and detecting thousands of more sources, (b) by measuring the remaining background flux, and (c) by determining the shape of the EGRB up to TeV energies. The many new ground-based detectors now under construction will supplement this information by discovering new extragalactic sources of gamma-rays of energies above 50 GeV.

On the other hand, the mystery of the origin of the EGRB in the MeV energy range must await a better determination of this background by a future dedicated satellite detector.