Selected aspects of recent progress in the study of supercooled liquids and glasses are presented in this review. As an introduction for nonspecialists, several basic features of the dynamics and thermodynamics of supercooled liquids and glasses are described. Among these are nonexponential relaxation functions, non-Arrhenius temperature dependences, and the Kauzmann temperature. Various theoretical models which attempt to explain these basic features are presented next. These models are conveniently categorized according to the temperature regimes deemed important by their authors. The major portion of this review is given to a summary of current experimental and computational research. The utility of mode coupling theory is addressed. Evidence is discussed for new relaxation mechanisms and new time and length scales in supercooled liquids. Relaxations in the glassy state and significance of the "boson peak" are also addressed.