This thesis presents a specialization of the integral equation (IE) method for the analysis of three-dimensional metallic and dielectric structures embedded in laterally unbounded (open) layered media. The method remains basically spatial but makes use of extensive analytical treatment of the vertical dependence of the problem in the 2D Fourier-transformed domain. The analytical treatment restricts somewhat the class of structures that can be analyzed. Still, the field of applicability remains very large, and includes most printed circuit and integrated circuit structures. The method is developed in full numerical detail, from first principles down to the properties of new Green's functions and the computation of particular types of convolution integrals. We show how the memory and time complexity are considerably reduced when compared to the requirements of the analysis of general 3D structures. With the newly developed tool, it is possible to deal with some peculiar characteristics of microwave and millimeter-wave circuits and antennas. Most noteworthy among these is the presence of thick metallizations (either electrically, or relative to circuit features). A novel full-wave analysis of arbitrarily shaped apertures in thick metallic screens is presented. This is compared to other methods, both full-wave and approximate, and demonstrated to offer excellent accuracy. Comparison with measured data, obtained from specially constructed prototypes, further validates the new technique. A second application is to the analysis of airbridges in coplanar waveguide (CPW) and slotline (SL) circuits. Comparison of measured and simulated data validates again our technique and provides valuable information about the behavior of CPW-fed slot loop antennas. Among the more specific applications, particular attention is devoted to the analysis and design of submillimeter-wave integrated dielectric lens feeds. These were object of study in the frame of a European Space Agency project, Integrated Front-End Receivers (IFER), which our Laboratory carried out in cooperation with a team at University of Toronto. The analysis method developed in this work encompasses and extends all previous work done at our Laboratory (LEMA) related with the analysis of this kind of feed. Together with the advanced 3D ray-tracing code developed at University of Toronto, it is possible to gain a high degree of insight into the behavior of these integrated receivers.