Exact results in QED

We consider several applications of the simplest nonlinear QED phenomena described by the light-by-light (LBL) scattering tensor. Among the relevant processes we present the splitting of high energy photon in a Coulomb field, calculate the asymptotics of differential photon photon elastic scattering. We show that LBL mechanism of the four photon mode of neutral pion decay have a dominant role compared, for instance, with the quark loop Feynman amplitude contribution. The mechanisms of creation of two and three gluon jets at colliding electro-positron beams is analyzed. We calculate also the contribution of LBL mechanism to the ortho-positronium decay width. One Of the important application is the analytic calculation of the QED contribution to the anomalous magnetic moment of the muon arising from LBL mechanism realized through electron positron loops, which is enhanced by the logarithm of the ratio of muon to electron masses. The modification of the QED kernel, which takes into account the QED polarization operator is used to extract the pure strong interaction contribution. We consider as well the problem of the Coulomb law modification. At second part of review we consider Moeller scattering process and RC to it. We show that RC are in agreement with renormalization group approach and could be taken into account in form of Drell-Yan process cross-section.