Abstract Although absorption of X-rays by matter has been observed since a long time, it is the recent availability of synchrotron radiation sources that has established EXAFS spectroscopy as an important structural tool in geosciences. Nowadays, X-ray Absorption Fine Structure (XAFS, including both the EXAFS and XANES domains) has proven to be an unquestionably useful and powerful method to obtain information on the local and medium-range structural order around a chemical element in condensed matter (solids, liquids, interfaces etc. ). This chapter provides basic information on EXAFS (Extended X-ray Absorption Fine Structure), including some recent experimental developments, both on data acquisition and on spectra reduction, and will be illustrated using recent applications in mineralogy, geochemistry, materials science and environmental science. XANES is separately discussed by Mottana (2004) in this volume. The experimental and theoretical details of extended X-ray absorption fine structure, EXAFS, have been extensively described in the literature ( e.g. Teo, 1986 ; Sayers & Bunker, 1987 ; Koningsberger & Prins, 1988 ; Lytle, 1989 ; Mustre de Leon et al. , 1991 ; Lytle, 1999 ). Recently, the technique has gained wide popularity, due to major breakthroughs both in EXAFS theory and data analysis with (i) the availability of convenient software packages (www.esrf.fr/computing/scientific/exafs/links.html) and (ii) the development of the use of the ab initio multiple scattering code FEFF ( Rehr & Albers, 1990 ; Zabinsky et al. , 1995 ; Ankudinov et al. , 1998 ; Ankudinov & Rehr, 2003 ).