This review is addressed to the development of lasers that might generate coherent radiation at ultrashort wavelengths by stimulating recoilless nuclear transitions in solids. First, the authors review the basic physics of stimulated emission, superradiance and the kinetics of lasing, with particular attention to those aspects that characterize recoilless nuclear transitions in solid hosts. Then they classify the various approaches to pumping that have been proposed for resolving the ``graser dilemma''---that the pump can destroy the conditions essential to gain---and discuss the general requirements for specification of an active nuclide and its solid host. The authors then classify and review those graser systems proposed since 1980 and prior to July 1996 in the published literature of the field, namely, (1) those that would pump directly, either with radiation or with intense bursts of neutrons; (2) those that would pump indirectly by first generating a nuclear isomer; (3) those that would eliminate the need for population inversion; and (4) several miscellaneous concepts. The significance of recent relevant experiments is described and discussed, and, finally, recommendations for future research are made.