Ultrarelativistic particles in strong crystalline fields of the order 1011 V/cm enable investigations of processes in fields of the order the QED critical field E0=m2c3/eħ=1.32·1016 V/cm. Utilizing the relativistic invariance of the parameter χ=γE/E0, where E is the local electric field, the field may become critical in the rest frame of an electron penetrating a single crystal. In the framework of the CERN NA63 experiment we have obtained experimental results on e.g. quantum synchrotron radiation emission, coherent pairs, radiation reaction and recently trident production in critical fields. With a corresponding critical magnetic field of B0=4.41·109 T such processes are also of astrophysical interest, e.g. in connection with magnetars. An overview of results from the CERN NA63 experiment is presented.