In this paper, we discuss the Transmission Line (TL) theory and its application to the problem of external electromagnetic field coupling to transmission lines. After a short discussion on the underlying assumptions of the TL theory, we start with the derivation of field-to-transmission line coupling equations for the case of a single wire line above a perfectly conducting ground. We also describe three seemingly different but completely equivalent approaches that have been proposed to describe the coupling of electromagnetic field coupling to transmission lines. The derived equations are extended to deal with the presence of losses and multiple conductors. The time-domain representation of field-to-transmission line coupling equations which allows a straightforward treatment of non linear phenomena as well as the variation in the line topology is also described. Finally, solution methods in frequency domain and time domain are presented.