In this chapter, we discussed the TL theory and its application to the problem of lightning electromagnetic field coupling to transmission lines. After a short discussion on the underlying assumptions of the TL theory, we described seemingly different but completely equivalent approaches that have been proposed to describe the coupling of electromagnetic fields to transmission lines. The field-to-transmission line coupling equations were then extended to deal with the presence of losses and multiple conductors and expressions for the line parameters, including the ground impedance and admittance were presented. The time-domain representation of the field-to-transmission line coupling equations, which allows for a straightforward treatment of nonlinear phenomena as well as the variation in the line topology, was also described. Solution methods in the frequency domain and in the time domain were given and application examples with reference to lightning-induced voltages were presented and discussed. Specifically, the effect of ground losses was illustrated and discussed. When the travelling voltage and current waves are originated from lumped excitation sources located at a specific location along a transmission line (direct lightning strike), both the corona phenomenon and ground losses result in an attenuation and dispersion of propagating surges along transmission lines. However, when distributed sources representing the action of the electromagnetic field from a nearby lightning illuminating the line are present, ground losses and the corona phenomenon could result in important enhancement of the induced voltage magnitude. Finally, we reviewed the theory of electromagnetic field coupling to a buried cable. Solution methods in the frequency and the time domain were also presented. Examples of lightning-induced currents and comparison with experimental data were presented.