This text comprises selected lectures presented in the 9th course of the International School of Cosmic-Ray Astrophysics held at the Ettore Majorana Centre in Erice, Sicily, May 7-18, 1994. Devoted to problems and prospects in high-energy astrophysics and cosmology, the major areas explored are: gamma- ray, X-ray, and neutrino astronomies; cosmic rays; pulsars and supernova remnants; and cosmology, as well as cosmogony. Among the principal developments in gamma-ray astrophysics are those generated by the Compton Gamma Ray Observatory. Cosmic neutrinos at MeV energies, i.e. those from the Sun and from Supernova 1987a are discussed, as well as neutrino masses in astrophysics. The source composition of cosmic rays and extensive air shower experiments receive special attention. The early universe according to COBE data, and as viewed by theorists of cosmology, is reviewed.