Passive remote sensing at microwave frequencies has applications which range from meteorology to oceanography and geology. The meteorological applications are the most fully developed and include measurements of the temperature profile of the atmosphere and of the atmospheric distribution of H2O and O3. Such measurements can he made from space or from the ground by utilizing the microwave resonances of O2, H2O, and O3which occur near 1-cm wavelength. Although infrared observations permit similar meteorological measurements, such optical devices are much more sensitive to aerosols and clouds. The small but finite nonresonant attenuation of most moderate clouds at microwave frequencies also permits their liquid water content to be estimated. At wavelengths longer than 2 cm the microwave properties of the terrestrial surface dominate observations from space, and measurements as a function of polarization and viewing angle yield information about surface temperature and emissivity. Such measurements of the ocean should also permit the sea state to he inferred. The review has two major parts. The first part reviews the physics of the interactions, the mathematics of data interpretation, and the instrumentation currently available. The second part is applications-oriented and emphasizes the types, accuracy, and relevance of possible meteorological measurements.