text: The physical process of non-linear inverse Compton scattering has been first introduced theoretically in different scientific articles starting from 1964. Before this date, some seminal works had emerged dealing with the description of the classical limit of NICS, called non-linear Thomson scattering or multiphoton Thomson scattering. In 1964, different papers  were published on the topic of electron scattering in intense electromagnetic fields by L. S. Brown and T. W. B. Kibble, and by A. I. Nikishov and V. I. Ritus, among the others. The development of the high-intensity laser systems required to study the phenomenon has motivated the continuous advancements in the theoretical and experimental studies of NICS. At the time of the first theoretical studies, the terms non-linear (inverse) Compton scattering and multiphoton Compton scattering were not in use yet and they progressively emerged in later works. The case of an electron scattering off high-energy photons in the field of a monochromatic background plane wave with either circular or linear polarization was one of the most studied topics at the beginning. Then, some groups have studied more complicated non-linear inverse Compton scattering scenario, considering complex electromagnetic fields of finite spatial and temporal extension, typical of laser pulses.
  The advent of laser amplification techniques and in particular of chirped pulse amplification (CPA) has allowed to reach sufficiently high-laser intensities to study new regimes of light-matter interaction and to significantly observe non-linear inverse Compton scattering and its peculiar effects. Non-linear Thomson scattering was first observed in 1983 with  keV electron beam colliding with a Q-switched Nd:YAG laser delivering an intensity of  W/cm (), photons of frequency two times the one of the laser were produced, then in 1995 with a CPA laser of peak intensity around  W/cm interacting with neon gas, and in 1998 in the interaction of a mode-locked Nd:YAG laser ( W/cm, ) with plasma electrons from a helium gas jet, producing multiple harmonics of the laser frequency. NICS was detected for the first time in a pioneering experiment  at the SLAC National Accelerator Laboratory at Stanford University, USA. In this experiment, the collision of an ultra-relativistic electron beam, with energy of about  GeV, with a terawatt Nd:glass laser, with an intensity of  W/cm (, ), produced NICS photons which were observed indirectly via a nonlinear energy shift in the spectrum of electrons in output; consequent positron generation was also observed in this experiment.
  Multiple experiments have been then performed by crossing a high-energy laser pulse with a relativistic electron beam from a conventional linear electron accelerator, but a further achievement in the study of non-linear inverse Compton scattering has been achieved with the realization of all-optical setups. In these cases, a laser pulse is both responsible for the electron acceleration, through the mechanisms of plasma acceleration, and for the non-linear inverse Compton scattering occurring in the interaction of accelerated electrons with a laser pulse (possibly counter-propagating with respect to electrons). One of the first experiment of this type was made in 2006 producing photons of energy from  to  keV with a Ti:Sa laser beam (W/cm). Research is still ongoing and active in this field as attested by the numerous theoretical and experimental publications.