Experimental results from the CERN NA43 and NA63 collaborations are presented, with particular emphasis on their relevance as a test-bed for the development of theory for e.g. beam-beam interactions in future accelerators. Crystals present a uniquely simple environment for the investigation of strong electromagnetic fields. When energetic charged particles are incident on crystals close to major crystallographic directions, the coherence of the crystalline field can produce very strong electric fields in the rest frame of the particle, exceeding the quantum critical field. In that domain, the radiation emission takes a substantial part of the electron energy and the spin of the electron strongly affects the synchrotron radiation spectrum. Similar effects are found theoretically in beamstrahlung in the planned future linear colliders, and crystals give the opportunity of experimental tests today.
