Classical electrodynamics (CED) and quantum electrodynamics (QED) are well established physical theories and their predictions have been confirmed experimentally in various regimes and with extremely high accuracy.

However, there are still areas of CED and of QED that deserve theoretical and experimental investigation, especially when physical processes occur in the presence of strong background electromagnetic fields. In the presence of electromagnetic fields of sufficiently high strength even the vacuum becomes unstable and electron-positron pair production spontaneously occurs. In view of the increasingly stronger available laser fields it is becoming feasible to employ them to test CED and QED under the extreme conditions supplied by intense fields.

After a broad introduction on CED and QED, I will describe different regimes of laser-matter interaction at ultra-high laser intensities and introduce present and upcoming experimental efforts to test the two theories under such extreme conditions.