I will give an overview of efforts to probe non-perturbative structures
in QED using intense laser fields, beginning with an introduction to the
Furry expansion of observables in strong backgrounds, which is the
basis of most modern theory calculations in "strong field QED". I will
then introduce the Ritus-Narozhny conjecture on the breakdown of exactly
those methods, and discuss its consequences and implications for theory
and future experiments using both laser-particle collisions and
beam-beam collisions. The talk will be introductory and details will be
kept to a minimum!