Charged particle motion and radiation in strong electromagnetic fields

Ultrastrong electromagnetic fields occur not only in astrophysical settings but also in dense lepton bunches, special crystals, and at the focus of high peak power lasers. For fields of sufficient magnitude including quantum electrodynamics effects becomes essential. Electron-positron pair creation and interaction of these pairs with the fields results in fascinating phenomena. In this review these particle dynamics are analyzed and shown to exhibit complex behavior including chaotic motion with strange attractors and limit cycles, as well as cascades where the vacuum ``explodes'' and acts back on the strong fields. An overview of planned experiments points to new discoveries which will challenge long-held theoretical expectations.