Utilizing the relativistic invariance of the parameter $\chi=\gamma\mathcal{E}/\mathcal{E}_0$, ultrarelativistic particles in strong crystalline fields $\mathcal{E}\lesssim10^{11}$ V/cm enable investigations of processes in fields of the order the QED critical field $\mathcal{E}_0=m^2c3/e\hbar=1.32\cdot10^{16}$ V/cm ($B_0=4.41\cdot109$ T) in the particle rest frame. In the framework of the CERN NA63 experiment we have obtained experimental results on e.g. quantum synchrotron radiation emission, trident production and coherent pairs in such fields, as well as observing effects related to the mesoscopic photon formation zone. Apart from their relevance to astrophysical emission processes as e.g.\ taking place at neutron stars and the fields encountered in heavy ion collisions, these studies are important for the design of the interaction point of future high energy colliders. Last, but not least, many of the processes studied are relevant in the context of intense laser fields, as e.g. aimed to be investigated at the Extreme Light Infrastructure (ELI).