The extragalactic diffuse emission at 
-ray energies has interesting
cosmological implications since the bulk of these photons suffer little or no
attenuation during their propagation from the site of origin.
Before the launch of the Compton Gamma-Ray Observatory (CGRO),
several balloon experiments
(White et al. 1977;
Schönfelder et
al. 1980)
and the -ray spectrometer
flown aboard three Apollo flights
(Trombka et al. 1977)
showed the presence of
a feature in the few MeV range, that was in excess of the extrapolated
hard X-ray continuum. At higher energies, above 35 MeV, the SAS-2 satellite
provided the first clear evidence for the existence of an extragalactic
-ray component
(Fichtel et al. 1975).
The first all-sky survey in low energy -rays (1 MeV - 30 MeV) has been
performed by COMPTEL and at higher energies, above 30 MeV, by EGRET on board
CGRO. The improved sensitivity, low
instrumental background and a large field of view of these instruments
have resulted in significantly improved measurements of the extragalactic
-ray
background. In the following I shall briefly summarize the recent
analysis results, and then I shall discuss the implications of these
new findings on the origin of the extragalactic diffuse emission and
current models thereof.