The physical nature, potentialities, and prospects of application of a new method of studying the structure of crystals and thin surface layers is discussed. It is based on recording secondary radiations such as external and internal photoelectron emission, as well as x-ray fluorescence, under conditions of dynamic x-ray diffraction in single crystals, in which the intensity of the radiation field in the crystal reproduces the periodicity of the crystal lattice in the form of a standing wave along the diffraction vector. The method allows one to measure the absolute displacements of atomic planes in the crystal in fractions of an Angstrom unit, and also to determine the degree of order in the arrangement of atoms in the surface layer. In addition to presenting the history of the problem and reviewing the most important studies published in this field in the past twenty years, the problems of the theory and the experimental technique of the method of standing x-ray waves are presented in considerable detail.