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 high-energy 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 all-sky γ-ray observatory beyond Milagro will be crucial for optimal science return in the multi-messenger age.