In this paper, full wave solutions are derived for the like- and cross-polarized electromagnetic fields diffusely scattered by two-dimensional rough surfaces. These expressions for the diffuse scattered fields are used to obtain the random rough-surface cross sections. The rough surface is characterized by a Gaussian joint probability density function for the surface heights and slopes at two points. These full wave results are compared with the associated small-perturbation results and physical optics results. They are also compared with experimental and numerical results (based on Monte Carlo simulations). The earlier assumption that the surface height and slopes can be considered to be uncorrelated is examined. The impact of using the large-radii curvature assumption and including self-shadow is also considered.