Hydrogenic (two-body) systems are the only atomic systems for which uncertainties in calculations of the energy levels approach the current state of the art in frequency measurement. This article discusses progress in the theory and measurement of transition frequencies in hydrogenic systems. These studies have relevance to the determination of fundamental constants and the testing of physical theories, especially quantum electrodynamics. A set of high accuracy calculable frequency standards could also be realized by using hydrogenic systems.