  In this article we review the progress made in understanding the main
characteristics of coherent \v{C}erenkov radiation induced by high energy
showers in dense media. A specific code developed for this purpose is described
because it took a significant part in this process. Subsequent approximations
developed for the calculation of radio pulses from EeV showers are reviewed.
Emphasis is given to the relation between the shower characteristics and
different features of the corresponding radio emission.
