The eikonal approximation has formed the basis for much of our understandings of the
interaction of light and electrons. The classical non-recoil approximation or quantum
mechanical Wolkow states of free – electron waves have been routinely employed to
interpret the outcomes of low-loss EELS or electron holography. Despite the
enormous success of semianalytical approximations, there are certainly ranges of
electron-photon coupling strengths where more demanding self-consistent analyses
are to be exploited to thoroughly grasp our experimental results. Slow-electron pointprojection
microscopes and many of the photoemission experiments are employed
within such ranges. We aim to classify those regimes and propose numerical solutions
for an accurate simulation model. A survey of the works carried out within selfconsistent
Maxwell-Lorentz and Maxwell-Schrödinger frameworks are covered here.
Several applications of the proposed frameworks are discussed, and an outlook for
further investigations is also delivered.