Surface nanostructuring enables the manipulation of many essential surface properties. With the recent rapid advancements in laser technology, a contactless large‐area processing at rates of up to m2 s−1 becomes feasible that allows new industrial applications in medicine, optics, tribology, biology, etc. On the other hand, the last two decades enable extremely successful and intense research in the field of so‐called laser‐induced periodic surface structures (LIPSS, ripples). Different types of these structures featuring periods of hundreds of nanometers only—far beyond the optical diffraction limit—up to several micrometers are easily manufactured in a single‐step process and can be widely controlled by a proper choice of the laser processing conditions. From a theoretical point of view, however, a vivid and very controversial debate emerges, whether LIPSS originate from electromagnetic effects or are caused by matter reorganization. This article aims to close a gap in the available literature on LIPSS by reviewing the currently existent theories of LIPSS along with their numerical implementations and by providing a comparison and critical assessment of these approaches. After more than five decades of research on laser‐induced period surface structures (LIPSS), the competition of the two different main theories (electromagnetics vs matter‐reorganization) is over: both approaches are currently merging into a coherent view on LIPSS. Depending on materials and irradiation conditions, aspects supporting one of the two theory classes can dominate the experimental observations.