Published online by Cambridge University Press: 27 June 2016
In this paper, conceptual points regarding electron elastic (Kapitza–Dirac effect) and inelastic diffraction effects on the slowed electromagnetic wave-structures/light-gratings are considered. From the unified point of view it is analyzed the main works on this subject for last four decades in chronological order, pointing out the essential peculiarity inherent in induced Cherenkov, Compton, and undulator/wiggler processes too. This review paper has also purpose to resolve confusion in scientific literature connected with the recently appeared paper Hayrapetyan et al. in 2015 regarding electron diffraction effect on a traveling wave in a dielectric medium.