Relativistic laser-matter interaction: From attosecond pulse generation to fast ignition

The field of laser-matter interaction has branched out in two main directions. The first, motivated by laser inertial confinement fusion, warm-dense-matter, fast ignition and astrophysics in laboratory, and the second driven by ultra-high intensity, exotic physics, high-energy particle, photon beam generation and time-resolved attosecond (zeptosecond) science. The degree of maturity from both experimental and theoretical stand-points is such that a large European infrastructure for each branch is contemplated as part of the European Roadmap. The first one, HiPER-PETAL will be dedicated to fast ignition with the aim of obtaining a thermonuclear gain of 100, whereas the second, Extreme Light Infrastructure (ELI) could go beyond the relativistic regime to foray into the ultra-relativistic domain >10²⁴ W cm^-2. In this paper we highlight the intriguing perspectives that these two projects will offer.