Conjecture of perturbative QED breakdown at $\alpha {\chi }^{2\mathrm{/}3}\gtrsim 1$

Invited talk given at Symposium “Extreme Light Technologies, Science, and Applications” (LPHYS’16, Yerevan, 11-15 July 2016). The old Ritus-Narozhny conjecture of possible breakdown of Intense Field QED perturbation theory for ultrarelativistic particles passing transversely through a strong electromagnetic field is reviewed with a special emphasis on its possible significance for near-future experiments.