Fundamental processes of quantum electrodynamics in laser fields of relativistic power

In this review we summarize our progress in the investigation of fundamental processes of quantum electrodynamics in laser fields of relativistic power in view of the more recent experimental progress in the generation of laser field intensities, yielding ponderomotive energy shifts U_p of the order of magnitude mc² and beyond. In particular, the generation of electron-positron pairs during the collision of laser pulses with ions or protons appears to become feasible.