Laser pulses can reach such high intensities nowadays that atoms exposed to them ionize virtually instantaneously. The extracted electrons are then accelerated to velocities nonnegligible to the speed of light. What remains are multiply charged ions with their most loosely bound outer electrons equally undergoing relativistic dynamics. These may temporarily escape from the vicinity of the ionic core, extract relativistic energies from the laser field and later recollide with the ionic core. The extremely large energies exchanged may be emitted in the form of coherent high-frequency light which is beneficial when an upconversion of frequencies is requested. Signatures of the magnetic field component of the laser field, the relativistic mass shift and spin-orbit coupling characterize the quantum relativistic dynamics. The existence of more than one active electron within the ion and that of more than one atom in gases or solids complicate the theoretical understanding considerably but simple pictures are often possible to a reasonable approximation.