Models of the Classical Electron after a Century

The point charge and the extended charge as models of the classical electron are studied. The problems inherent to each model with respect to self-interaction are disclosed and the possible solutions are analysed. The possible relation between these models is also discussed. We argue that a totally electromagnetic electron, as well as a point electron, is beyond the scope of classical electrodynamics. This work is intended as a complement to F. Rohrlich's recent account in the sense that it points at challenges still present in the way to a deeper understanding of the electron.