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.

LaTex file, 22 pages, 1 Postscript figure