The statistical properties of gamma-ray emitting AGN are discussed, based on radio sources stronger than 1 Jy at 5 GHz that have been detected by the EGRET experiment on the Compton Gamma Ray Observatory. Most strong gamma-ray sources are radio quasars; radio galaxies are a small component of the population. Among the 1 Jy quasars, gamma-ray detections have stronger than average radio flux, but are not unusually compact or flat spectrum. The redshift distributions of gamma-ray detections and nondetections are indistinguishable. The energy budget of radio quasars detected by EGRET is dominated by gamma-rays. A model is constructed where radio and gamma-ray flux densities are weakly correlated, as observed, but with a large scatter much of which may be due to variability. Using this model to fit the EGRET detection rate in the 1 Jy sample, it is predicted that the gamma-ray detections arise from the high S-gamma/S-r tail of the radio source population, and that many radio sources must emit gamma-ray fluxes not far below the EGRET sensitivity limit. Radio quasars contribute similar to 50% of the diffuse extragalactic background; optically selected QSOs must contribute 5% or less. Most of the flux and variance due to unresolved point sources is contributed by radio sources in the range 0.05<S-rad<0.5 Jy. The data are broadly consistent with Doppler-boosted emission from a relativistic jet at both gamma-ray and radio wavelengths. (C) 1996 American Astronomical Society.