Recent advances in the methods of structural analysis, in particular the use of particle accelerators to produce pulsed neutrons and synchrotron radiation, have greatly improved our ability to describe the atomic structure of nonperiodic matter quantitatively using the atomic pair distribution analysis, or the real-space method of powder diffraction. The method can now be applied to crystalline or nearly crystalline solids as well to describe deviations from perfect periodicity with a sufficient accuracy. We discuss the fundamental issues pertaining to the use of this technique, and review some of the recent results obtained by this method in the fields of high-Tc oxide superconductors, quasicrystals and metallic glasses. © 1990, The Japan Institute of Metals. All rights reserved.