In most practical problems involving radio wave transmission through precipitation, the average, or coherent, field is one of the most important quantities. Although the classical formulation describing coherent propagation effects such as attenuation has existed for many years, it is only recently that this formulation has been extended to adequately include polarization effects. In the last 10 years, a number of theories that take into account the polarization effects caused by the random orientations of the precipitation scatterers have been developed. The similarities and differences between these theories, however, and the role of multiple scattering, are not yet well understood. This paper reviews recent work on the subject. Emphasis is placed on a clarification of (1) the similarities and differences of the various generalizations to the classical theory and (2) the role of multiple scattering in both the classical theory and these generalizations and their approximations. Some improvements to existing theories are also presented.