This book presents an overview of theory and recent advances concerning the shadowing function, an important element in the simulation and calculation of electromagnetic waves scattering at randomly rough surfaces. The authors address derivation of the shadowing function, helping researchers to understand the theoretical aspects of the problem, while applications of the shadowing function are discussed to show how it is applied to real problems. Ideal for graduate students and researchers working on high frequency scattering, infrared radiation, reflectivity and ray-tracing techniques from rough surfaces.