The commonplace use of non-metallic materials and composites in vehicles and other environments has led to a need to compute scattering and other electromagnetic phenomena in their presence. This text provides comprehensive treatment of a variety of approximate boundary conditions in electromagnetics. The genesis and properties of impedance, resistive sheet, conductive sheet, generalized and absorbing boundary conditions are discussed. Applications to diffraction by numerous canonical geometries and impedance structures are presented. Accuracy and uniqueness issues are addressed, and high frequency techniques such as the physical and geometrical theory of diffraction are introduced.