Among ray-finned fishes that provide parental care, many spawn in constructed nests, ranging from bowls, burrows and ridges to nests made of algae or bubbles. Because a nest by definition is a construction that enhances the nest-builder's fitness by helping it meet the needs of the developing offspring, nest-building behaviour is naturally selected, as is a preference for spawning with mates that provide well-built nests. However, nest-building behaviour can also be sexually selected, when nest traits increase mating success, protect against sperm competition or nest take-overs by conspecifics. Here, we offer a systematic review, with examples of how competition for sites and location of fish nests relates to sexual selection. We examine direct and indirect benefits of mate choice linked to nest traits, and different types of nests, from a sexual selection perspective. Nest-related behaviours are often under both natural and sexual selection, and we disentangle examples where that is the case, with special attention to females. We highlight some taxa in which nest building is likely to be sexually selected, but lack of research has left them uninvestigated. Some of them are established aquarium species, making them particularly amenable for future research. Finally, we compare with arthropods, amphibians and birds.This article is part of the theme issue ‘The evolutionary ecology of nests: a cross-taxon approach’.