Our knowledge of the high-energy universe is undergoing a period of rapid change as new astronomical detectors of high-energy radiation start to operate at their design sensitivities. Now is a boomtime for high-energy astrophysics, with new discoveries from Swift and HESS, results from MAGIC and VERITAS starting to be reported, the upcoming launches of the γ -ray space telescopes GLAST and AGILE, and anticipated data releases from IceCube and Auger.A formalism for calculating statistical properties of cosmological γ -ray sources is presented. Application is made to model calculations of the statistical distributions of γ -ray and neutrino emission from (i) beamed sources, specifically, long-duration GRBs, blazars, and extragalactic microquasars, and (ii) unbeamed sources, including normal galaxies, starburst galaxies and clusters. Expressions for the integrated intensities of faint beamed and unbeamed highenergy radiation sources are also derived. A toy model for the background intensity of radiation from dark-matter annihilation taking place in the early universe is constructed. Estimates for the γ -ray fluxes of local group galaxies, starburst, and infrared luminous galaxies are briefly reviewed.Because the brightest extragalactic γ -ray sources are flaring sources, and these are the best targets for sources of PeV-EeV neutrinos and ultra-high energy cosmic rays, rapidly slewing all-sky telescopes like MAGIC and an allsky γ -ray observatory beyond Milagro will be crucial for optimal science return in the multi-messenger age.C.D. Dermer ( ) Code 7653,