This paper reviews experimental and theoretical research on cross polarization that occurs during clear-air conditions on terrestrial microwave links. After consideration of the various clear-air mechanisms that have been suggested, the conclusion is drawn that multipath mechanisms interacting with the cross-polarized patterns of the antennas are the most important. Theoretical models that explain these mechanisms and semi-empirical models that characterize the cross-polarized signal statistics are then discussed. Particular attention is given to the semi-empirical models since they can be used most readily for statistical predictions in design applications. Some new insight into the similarities and differences between models developed in France, Japan, and the United States is provided. Finally, application of the semi-empirical models in the design of digital systems is briefly considered, and the relative importance of cross polarization during clear-air and precipitation conditions is discussed.