The Current Status of the LeptongFactors

The past three years have seen new measurements of the $g$-factor anomalies of the free leptons ($e^{\pm }, {\mu }^{\pm }$). At the same time there have been several major theoretical advances including a quantum electrodynamic calculation of the sixth-order coefficient of the electron anomaly. In this article we review these recent developments in detail, however we also: (1) present a historical overview of $g$-factor measurements and their interpretation since the early days of quantum theory, (2) discuss several experiments which are currently being attempted but which have not yet yielded results of high precision, (3) attempt to predict the most likely course of $g$-factor research in the near future. An extensive Bibliography and Tables summarizing both historical events and current work are included.