In 1912 x-ray diffraction in crystals was discovered, and soon afterwards the structures of rock salt and diamond were determined. This laid the foundation of x-ray structure analysis introducing the physicists to the world of atomic structures of crystals. Later on, two more similar methods -electron and neutron diffraction -came into being.From the mathematical standpoint, the diffraction of short-wave coherent radiation by systems of atoms is the problem of finding the wavefront and intensity in the process of scattering. The determination of the structure of an object from the experimentally observed diffraction field is the reverse problem. It reduces to the solution of complicated sets of equations or integral equations and often has no unambiguous solutions. Both diffraction theory and structure analysis are applied not only to single crystals, but also to less ordered systems, e.g. polycrystals, liquid crystals, solutions of molecules and macromolecules, to liquids and amorphous solids, and finally, to gases.Structure analysis uses various experimental methods. These depend essentially on the ordering of the substance studied and on the type of radiation used. These methods will be the subject of the present chapter.