Laser-induced periodic surface structures (LIPSS) are a simple and robust route for the nanostructuring of solids that can create various surface functionalities featuring applications in optics, medicine, tribology, energy technologies, etc. While the current laser technologies already allow surface processing rates at the level of m2/min, industrial applications of LIPSS are sometimes hampered by the complex interplay between the nanoscale surface topography and the specific surface chemistry, as well as by limitations in controlling the processing of LIPSS and in the long-term stability of the created surface functions. This Perspective article aims to identify some open questions about LIPSS, discusses the pending technological limitations, and sketches the current state of theoretical modelling. Hereby, we intend to stimulate further research and developments in the field of LIPSS for overcoming these limitations and for supporting the transfer of the LIPSS technology into industry.