Advances in the theory of atmospheric tides since the monograph by Chapman and Lindzen (1970) are comprehensively reviewed. Major developments include investigations of the effects of mean zonal winds and meridional temperature gradients, molecular viscosity and thermal conductivity, radiative damping, composition variations, and hydromagnetic coupling, including seasonal and solar cycle effects. Linearized inviscid and viscid equations of general applicability are documented in this review, and a number of quantitative studies of atmospheric tides are considered as simplifications or modifications of these equations. Recent calculations of thermal excitation due to insolation absorption by H2O and O3 below 80 km, UV and EUV absorption in the lower thermosphere, and latent heat release in the tropical troposphere are presented. Although no attempt is made to exhaustively review incoherent scatter, meteor radar, and satellite mass spectrometer contributions to the study of atmospheric tides, representative wind, temperature, and composition data from these sources are interpreted within the framework of the most recent quantitative models, and the current status of our understanding of atmospheric tides is assessed. Some potentially fruitful areas of future research are also presented. Copyright © 1979 by the American Geophysical Union.