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!