XAFS is a fine structure that appears after the absorption edge of the X-ray absorption spectrum, and is known to reflect the local structure and electronic state of X-ray absorbing atoms. XAFS is an extremely powerful method for structural analysis of materials without crystallinity, and is currently widely used for the characterization of nanoparticles, catalytically active species, and trace elements in glasses. In this review, I briefly explain the principle and measurement method of XAFS, and introduce examples of its application to heterogeneous solid powder catalysts and metal nanoclusters, centering on the author's research results.