Considerable efforts have been made in the past to characterize the coupling of an electromagnetic wave to a structure, the simplest configuration being a cable parallel to the ground surface. If the height of the wire above ground is smaller than the free-space wavelength of the disturbing signal, the transmission-line theory is often used but since the ground impedance is frequency dependent, recent works have been done to model correctly the ground in the time-domain. Furthermore the incident field propagating along the ground surface may be distorted by obstacles such as hills and valleys and the effect of terrain topography may play a leading role in certain configurations. The interaction with the system itself has often be treated by considering separately the external and internal interaction. The objective of the topological approach is to get both a quantitative tool to relate the external signal to a response somewhere within the system and a qualitative one allowing a clear decomposition of the system in terms of successive shields and penetration paths. The latest developments and suggested further studies are outlined