This text focuses on the nonlinear properties of nanostructured systems that arise as a result of optical wave mixing. The authors present a review of nonlinear optical processes on the nanoscale and provide theoretical descriptions for second and third-order optical nonlinearities in nanostructures such as carbon allotropes, metallic nanostructures, semiconductors, nanocrystals, and complex geometries. Here, the characterization and potential applications of these nanomaterials are also discussed. The factors that determine the nonlinear susceptibility in these systems are identified as well as the influence of physical mechanisms emerging from resonance and off-resonance excitations. In addition, the authors detail the effects driven by important phenomena such as quantum confinement, localized surface plasmon resonance, Fano resonances, bound states, and the Purcell effect on specific nanostructured systems. Readers are provided with a groundwork for future research as well as new perspectives in this growing field. weiterlesen