Following an outline of electromagnetic transients in high-voltage power networks, together with their principal implications in relation to system overvoltages and the switching duty imposed on circuit-breakers, the paper develops a broad review of the now numerous analysis formulations and computer solution methods in this area of applied analysis in power systems. The perspective is one which extends from the earliest developments in surge analysis to the most recent proposals from current research. In particular, it includes the main forms of traveling-wave methods, Bergeron analysis, time-convolution schemes, and the recently derived methods in which the z transform has a unique part.