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This presentation reviews current and expected developments in the field of laser-induced periodic surface structures (LIPSS, ripples). These surface nanostructures are a universal phenomenon and can be generated on almost any material by irradiation with intense linearly polarized radiation. LIPSS are formed in a “self-ordered” way and are often accompanying laser material processing applications. The structures can be produced in a single-step process and enable surface functionalization through the adaption of optical, mechanical and chemical surface properties. Their spatial periods typically range from several micrometers down to less than 100 nanometers, exhibiting a clear correlation with the polarization direction of the laser radiation used. Various types of LIPSS have been classified, relevant control parameters were identified, and material specific formation mechanisms are analyzed for different types of inorganic solids, i.e., metals, semiconductors, and dielectrics, through time-resolved optical experiments and theoretical simulations. Special attention will be paid to a comparison of the currently available formation theories for LIPSS with a discussion of their respective strengths and weaknesses. Currrently explored applications featuring surface functionalization in the fields of optics, surface wetting, medicine, and tribology will be discussed.