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In recent years, a large number of papers have appeared that dealt with$\EPEM$ pair production in heavy ion collisions at high energies. To a largeextent these studies were motivated by the existence of relativistic heavy ionaccelerators all over the world. There pair production can be studied in socalled ``ultra-peripheral collisions'', where the ions do not come close enoughto interact strongly with each other. Various different methods have been usedand it is the purpose of this review to present a unified picture of thepresent status of the field.

Electron-Positron Pair Production in Relativistic Heavy Ion Collisions