  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 gamma-ray space
telescopes GLAST and AGILE, and anticipated data releases from IceCube and
Auger. A formalism for calculating statistical properties of cosmological
gamma-ray sources is presented. Application is made to model calculations of
the statistical distributions of gamma-ray and neutrino emission from (i)
beamed sources, specifically, long-duration GRBs, blazars, and extagalactic
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 gamma-ray fluxes
of local group galaxies, starburst, and infrared luminous galaxies are briefly
reviewed. Because the brightest extragalactic gamma-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 gamma-ray observatory beyond Milagro will be crucial for optimal
science return in the multi-messenger age.
