  The quantum field theory in the presence of classical background
electromagnetic fields is reviewed. We give a pedagogical introduction to the
Feynman-Furry method of describing non-perturbative interactions with very
strong electromagnetic fields. A particular emphasis is given to the case of
the plane-wave electromagnetic field for which the charged particles' wave
functions and propagators are presented. Some general features of quantum
processes proceeding in the intense electromagnetic background are argued. We
also discuss the possibilities of searching new physics through the
investigations of quantum phenomena induced by the strong electromagnetic
environment.
