Due to size constraints, the present review is necessarily limited in its coverage. We restrict consideration to recent theoretical developments in the kinetics of supercooled liquids and glasses and, in particular, to those theories that arc in some sense microscopic. Hence, little attention is given to advances in phenomenological theories of glassy relaxation, which have proven to be quite valuable in the prediction of material behavior. Readers interested in such theories are referred to the excellent books by Brawer (1) and Scherer (2), and to the original papers (3-5). We also provide limited discussion of the many structural or packing models that have been proposed for amorphous solids (6-9). Although short-ranged frustration arising from packing constraints undoubtedly contributes to the sluggish dynamics of glassy systems, these models do not directly address the kinetics of structural relaxation considered here. Some discussion of structural models is given in the recent review article of JackIe (10) and by several authors in the three New York Academy of Sciences volumes on glasses (11-13). In the present review we use the term structural glass (STG) to refer to conventional amorphous materials with configurational disorder, pre pared for example by quenching a liquid. The glass transition phenomena in STGs have some similarities to, but are in many ways distinct from, corresponding phenomena observed in so-called spin glasses (25, 26). We focus exclusively on conventional STGs throughout the manuscript. Finally, the present review gives little attention to computer simulation methods for the investigation of structural relaxation. The extent to which