X-ray absorption fine structure spectroscopy is widely used for local structure determination for various inorganic compounds and called extended X-ray absorption fine structure (EXAFS). This article describes recent advanced techniques and applications of X-ray fine structure absorption spectroscopy, including EXAFS and edge structure for heterogeneous catalysts. The correlation between the structure of surface active site and the chemical state is focused for cobalt, molybdenum, and selenium catalysts. In a sense that the spectroscopy approaches chemical state of reaction intermediates and their reactivity, X-ray absorption spectroscopy is one of the most powerful "chemical probe" for surface catalytic chemistry.