The scattering of waves by random rough surfaces has important applications in remote sensing ofoceans and land. The problem of developing a model for rough surfaces is very difficult since, at best,the scattering coefficient σ 0 is dependent upon (at least) radar frequency, geometrical andphysical parameters, incident and observation angles, and polarization. The problem of electromagneticscattering from a random rough surface is analyzed using the Kirchhoff approximation (stationary phase,scalar approximation), the small perturbation model and the two-scale model. The first major newconsideration in this paper is the polarimetric signature calculation as a function of the transmitterlocation and receiver location for a bistatic radio- link. We calculate the like- and cross-polarizedreceived power directly using the scattering coefficients, without calculating the Mueller matrix. Next,the study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the modelsare made for various of the surface height rms and correlation length both normalized to the incidentwave number (denoted by σ and L, respectively). By using these two parameters to form atwo-dimensional space, the approximate regions of validity are then established. The second major newconsideration is the development of a theoretical two-scale model describing bistatic reflectivity aswell as the numerical results computed for the bistatic radar cross-section from rough surfaces especiallyfrom the sea and snow-covered surfaces. The results are used to show the Brewster angle effect onnear-grazing angle scattering.