X-ray absorption fine structure (XAFS) is a powerful tool in the study of the local atomic environment in condensed matter. It has been often applied to the study of advanced materials and nanostructures, significantly contributing to their characterization at the local level and to the understanding of the relation between atomic structure and physical properties. This lecture begins with quick overview of XAFS (including both EXAFS and XANES or NEXAFS) as a tool for the determination of local structure, stressing its advantages and limitations (i.e. when it should and when it should not be used) and its role in the interplay between materials growth (synthesis), physical properties and characterization. A brief summary of the various experimental set-ups and detection schemes which can be used in the field of materials science follows. The main part of the lecture consists in a review of the use of XAFS to study advanced materials and nanostructures. Some of the topics covered include: • Dopants and defects in semiconductors. In clear illustration of the characteristics and advantages of XAFS, it has highlighted the connection between local structure and the generally observed saturation in carrier concentration at high dopant levels. Specific examples include arsenic in silicon and silicon in gallium arsenide delta-doped heterostructures. Recent research on hydrogen – nitrogen complexes in GaAsN dilute nitride alloys is described. • Semiconductor alloys. XAFS has detected and described the existence of local structural distortions in semiconductor alloys and its connection with long range order; the textbook example of InGaAs alloys and recent research on dilute magnetic semiconductors are illustrated. • Amorphous solids. Due to its local and chemical sensitivity, XAFS has played an important role in the study of amorphous materials and specifically the quantification of atomic ordering phenomena. Specific examples include amorphous group IV semiconductor alloys. The relation with X-ray scattering investigations is discussed. • Thin films, interfaces and surfaces. A high surface sensitivity can be obtained in specific experimental set-ups and this has been exploited in numerous investigations. Examples include cubic and hexagonal GaN thin films and the interfaces between ferromagnetic and antiferromagnetic materials (Fe/NiO). • Oxides and highly correlated materials. The complex interplay between local distortions and physical properties in materials such as manganites, as studied by XAFS, will be described. • Thermal vibrations. XAFS can measure with high accuracy temperature dependent structural properties (bond lengths and their distribution). Examples include anharmonic vibrations in AgI and Ge. • Nanostructures. In this field XAFS can be used to study interdiffusion phenomena and dependence of local structure on the dimensions. Examples include Ge quantum dots on Si, porous Si, semiconductor nanoparticles embedded in silica, metallic clusters and core-shell nanostructures.