IZEST looks beyond the horizon set by ELI. During this meeting we will have the opportunity to describe the most avant-garde laser concepts under development to gracefully segue from the petawatt to the exawatt, giving access to extremely short time structures down to the attosecond-zeptosecond regime. Pulses will be so short that the highest peak power in the x-ray regime could be reached with a modest amount of energy in the joule level yielding intensities in the Schwinger regime enough to materialize light. Among the remarkable application we note the generation of gargantuan accelerating gradients in solids enough to accelerate electrons over a centimetre to the TeV level or relativistic protons widening the range of applications in subatomic physics, cosmology, vacuum physics and the like. In addition, trying to develop a new breed of laser sometime opens the way to new applications, like space debris removal which is a big issue in space activity in the near future.