The progress in technology of the ultrahigh power lasers gave physicists a new tool for exploring new extreme regimes of interaction between electro- magnetic field and matter, as well as resulting extreme states of matter. With the development of petawatt class lasers and implementation of techniques for better focusing (adaptive optics, such as deformable mirrors) intensities of ~ 10²³ W/cm² should become available in the near future. The electric field of a laser focused to the intensity of 10²¹ W/cm² can accelerate an electron from rest to ultra-relativistic energies of hundreds of MeV within a fraction of the laser period. What happens to electrons bound in atomic or ionic systems at these intensities is not quite clear and existing th...