The author has performed a review of the literature pertinent to wave scattering from rough surfaces. The early techniques developed for this problem are discussed, including the perturbation technique and the Kirchhoff approximation. The limitations of such models are highlighted. The developments in the theory, since the introduction of these models, are also given. These include: the effects of shadowing; multiple scattering effects; integral equation techniques and variational methods. Results from experimental investigations of rough surface scattering are also reviewed. These results are compared with the theoretical predictions. A brief review is also given of the methods by which the profiles of rough surfaces are measured and the problems inherent in making these measurements. A comparison is made between the assumed profiles, used in the theory, and the measured profiles.