Quantum regime of laser-matter interactions at extreme intensities

A survey of physical parameters and of a ladder of various regimes of laser-matter interactions at extreme intensities is given. Special emphases is made on three selected topics: (i) qualitative derivation of the scalings for probability rates of the basic processes; (ii) self-sustained cascades (which may dominate at the intensity levels attainable with next generation laser facilities); and (iii) possibility of breaking down the Intense Field QED approach for ultrarelativistic electrons and high-energy photons at certain intensity level.