The activity in the research on novel optical materials exhibiting nonlinear optical (NLO) properties is surveyed, especially nonlinear absorption, that may be attractive for various applications, including those in optoelectronics, photonics, and biophotonics. The recently introduced concept of “NLO pigments”—insoluble colored materials that can exhibit useful NLO effects—is demonstrated to apply to the multifunctional group of coordination polymers (CPs) and their subgroup of metal‐organic frameworks (MOFs), which may be applied in their microcrystalline form or as nanoparticles. Nanocrystalline materials such as semiconductor quantum dots or plasmonic particles made of noble metals have been widely studied and their properties have been often reviewed, thus they are not included in this review. On the other hand, studies performed on perovskites are described: materials that appear to have great potential for NLO applications in addition to their well‐known merit in photovoltaics. There is also much activity in the field of low‐dimensional, especially 2D structures of various kinds, and this review covers many examples of such structures, not including the broad topic of carbon nanostructures (graphene, nanotubes etc.) but concentrating on other emerging nonlinear optical materials such as black phosphorus, transition metal dichalcogenides, MXenes, and topological insulators.