The adiabatic approximation has formed the basis for much of our understandings of the interaction of light and electrons. The classical nonrecoil approximation or quantum mechanical Wolkow states of free-electron waves have been routinely employed to interpret the outcomes of low-loss electron energy-loss spectroscopy (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 point-projection microscopes and many of the photoemission experiments are employed within such ranges. Here, we aim to classify those regimes and propose numerical solutions for an accurate simulation model. A survey of the works carried out within self-consistent Maxwell-Lorentz and Maxwell-Schrödinger frameworks are outlined. Several applications of the proposed frameworks are discussed, and an outlook for further investigations is also delivered.