Over the last three decades low-dimensional systems have attracted increasing interest both from the fundamental and technological points of view due to their unique physical and chemical properties. X-ray absorption spectroscopy (XAS) is a powerful tool for the characterization of such kinds of systems, owing to its chemical selectivity and high sensitivity in interatomic distance determination. Moreover, XAS does not require long-range ordering, that is usually absent in low-dimensional systems. Finally, this technique can simultaneously provide information on electronic and local structural properties of the nanomaterials, significantly contributing to clarify the relation between their atomic structure and their peculiar physical properties. This review provides a general introduction to XAS, discussing the basic theory of the technique, the most used detection modes, the related experimental setups and some complementary relevant characterization techniques (diffraction anomalous fine structure, extended energy-loss fine structure, pair distribution function, x-ray emission spectroscopy, high-energy resolution fluorescence detected XAS and x-ray Raman scattering). Subsequently, a selection of significant applications of XAS to two-, one-and zero-dimensional systems will be presented. The selected low-dimensional systems include IV and III-V semiconductor films, quantum wells, quantum wires and quantum dots; carbon-based nanomaterials (epitaxial graphene and carbon nanotubes); metal oxide films, nanowires, nanorods and nanocrystals; metal nanoparticles. Finally, the future perspectives for the application of XAS to nanostructures are discussed.