Last March marked the seventieth birthday of the eminent physicist and leader of Soviet science, the great public figure, Academician Sergei Ivanovich Vavilov, who passed away ten years ago. The scientific community took note of this date by holding a series of scientific conferences. We print in this issue several papers read at the joint meeting of the Presidium of the U.S.S.R. Academy of Sciences and the scientific community on March 24. Some of the reports read at conferences held at the P. N. Lebedev Physics Institute and the S. I. Vavilov Optics Institute in connection with this occasion, are also here.