This article reviews the astrophysics and cosmological evidence for nonbaryonic dark matter (DM). It covers historical, current, and future experiments that look for direct evidence of particle DM. In addition, it surveys the underlying particle theories that provide some guidance about expected event rates, and the future prospects for the discovery of DM. A number of recent theoretical papers, making calculations in SUSY-based frameworks, show a spread of many (>5) orders of magnitude in the possible interaction rates for models consistent with existing cosmological and accelerator bounds. Within this decade, it seems likely that DM searches will be successful, or at the very least rule out a broad class of the currently most favored DM models.