Some recent results from CERN-experiments are described. The paper discusses the emission of radiation from GeV electrons and positrons traversing thin Si and Ge crystals. The special features of radiation emission and pair production in the multi GeV region is discussed. Dramatic energy losses are found for well aligned electrons. The combined process of radiation emission and pair production result in shower formation which along crystalline directions is strongly enhanced—leading to radiation lengths that are (20–50) times shorter than those for amorphous materials. Strong crystalline fields might turn out to be the best way to extract TeV-beams from coming accelerators and to determine accurately the origin of GeV-TeV gamma rays from the universe.