The application of the Fourier transformation method to the measured EXAFS (Extended X-ray Absorption Fine Structure) curve has made it possible to determine the local atomic arrangement around an absorbing atom in crystalline and amorphous materials. A review has been made on the principle, characteristics and difficulties of this new method. A few variational methods of measuring the EXAFS curves are also described. Interesting results so far published are mentioned on various materials, including superconductors, catalysers and biologically important protein molecules, in crystalline, amorphous, dissolved and adsorbed states. The results obtained by the polarized X-rays and the structural changes under high pressure are also described. Finally, the relation between this EXAFS method and the X-ray diffraction method is illustrated from the viewpoint of X-ray anomalous scattering.