In this review paper, the principal steps in the derivation of the full wave solutions to problems of scattering and depolarization by irregular layered media are presented. Special consideration is given to scattering by two-dimensional random rough surfaces of finite conductivity. The full wave solutions are compared with the high-frequency/geometric optics and physical optics solutions as well as the low-frequency/perturbation solutions. Since the full wave approach accounts for both specular point scattering as well as diffuse/Bragg scattering in a unified self-consistent manner, it resolves the discrepancies between the physical optics and perturbation solutions and bridges the wide gap between them. Thus on applying the full wave approach to scattering by composite rough surfaces, it is not necessary to adopt a two-scale model of the rough surface. The full wave solutions are also compared with hybrid perturbation and physical opticssolutions which are based on the artificial decomposition of the composite rough surface into a large- and a small-scale rough surface. The full wave solutions satisfy duality, reciprocity, and realizability relationships in electromagnetic theory, and the results are invariant to coordinate transformations. The full wave approach also accounts for coupling between the radiation fields, the lateral waves, and the surface waves that constitute the complete field expansions, and it can be applied to problems of scattering at near-grazing angles. A recent review of the full wave approach is also discussed in detail. ¿American Geophysical Union 1987