  The adiabatic 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 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 Schrodinger frameworks are
outlined. Several applications of the proposed frameworks are discussed, and an
outlook for further investigations is also delivered.
