This article is a survey of the theoretical background for full-wave spectral-domain analysis of open microstrip discontinuities of arbitrary shape. The spectral-domain dyadic Green's function, which takes into account all the physical effects, such as radiation and surface waves, is used to formulate an electric field integral equation. The method of moments is then employed to find the current distribution on the microstrips, and subsequently, the scattering parameters of the junctions. Since all field components can be expressed in terms of the dyadic Green's function and the current distribution, the losses due to both radiation and surface waves are further determined through a rigorous Poynting vector analysis. To model the discontinuities of arbitrary shape, both rectangular and triangular subdomain functions are used as the current expansion functions in the moment method procedure. In addition, the semi-infinite traveling wave functions are applied to simulate the feeding structure and isolate individual junction effects. Several examples are demonstrated to illustrate the utility of different techniques in this analysis. Comparison of some numerical results with available experimental data shows excellent agreement. Finally, this approach is most natural for the characterization of 3-D integrated circuits and the design of printed antennas including excitation circuit effects.