The mode-matching method is a useful technique for formulation of boundary-value problems, especially for structures consisting of two or more separate regions. It is based on matching the fields at the boundaries of different regions and hence lends itself naturally to the analysis of microwave boundary-value problems. The mode-matching method has widely been used for scattering and transmission problems, as well as transmission line analysis. Scattering problems include discontinuities in waveguides and transmission lines, such as the microstrip line and the coplanar waveguide (CPW), and obstacles in a medium. Transmission problems include analysis of filters, such as fin line bandpass filters, impedance transformers, and power dividers and transitions such as waveguide-to-microstrip line. Transmission line analyses include determination of the transmission line's propagation constant and characteristic impedance, such as those of a microstrip line, a CPW, and coplanar strips (CPSs). In this chapter, we describe the mode-matching method for analyzing planar transmission lines. Coplanar strips with finite strip metallization thickness are used to illustrate the formulation process. We also describe the mode-matching method for the analysis of planar transmission line discontinuities. A CPW is used to serve this purpose.