An overview of the problems involved in the study of electromagnetic power transmission between lossy media is presented. Starting from the well-known problem of the transmission at a dielectric-conductor interface, the different representations of the complex propagation vector of the plane waves are introduced. Analytical expressions to convert from one formulation to the other are obtained. Moreover, the transmission of a plane wave at the interface between two lossy media is taken into account. An explanation of the strange behavior of the transmitted wave is developed by means of power considerations. Finally, the interesting effect of the parallel-attenuated transmitted wave is presented, and its properties as a function of the incident phase vector amplitude are deduced.