The aim of this proposal is to request support for two EuroConferences devoted to new advances in the study of the interaction of matter with extremely intense laser light. Indeed, the recent development of powerful femtosecond lasers makes it now possible to achieve enormous intensities, of the order of 10, 19 W/cm². In these conditions, the electric field of light is stronger than that present inside the atoms and causes the electrons to move at velocities very close to the speed of light. This leads to a variety of new phenomena, many of which are not yet well understood. The technology is evolving rapidly and new experiments are being performed, creating a need for a new and deeper theoretical interpretation. European research is holding the world leadership in this fast growing area of research.