In the present contribution we review some recent work on scattering of electromagnetic waves from various geophysical targets, by means of P. C. Waterman's approach. As an introduction to the specific applications to be described, a general outline is given of the basic features of this approach, as applied to electromagnetic waves. The algebraic structure of the resulting equations for single and multiple scattering situations is discussed with special emphasis on the case of an infinite interface and an adjacent finite inhomogeneity in one of the half spaces. We review a number of applications relevant for electromagnetic prospecting. The bedrock is modeled as a lossy half space, and various configurations of ore bodies in this half space are considered. The measurements are assumed to be made on the surface or along a borehole into the ground, and the radiation source is again either on the ground or in the borehole. The behavior of the field in the vicinity of the inhomogeneity and interference effects are discussed. Actual ore bodies are often rather thin plates, and the influence of a layered structure of the half space may be of importance. Therefore in other applications the half space is taken to be layered, and the inhomogeneity is taken to be a perfectly conducting spheroid or a perfectly conducting disc.