Billions of fishes are kept in captivity for research and food production world‐wide, with a strong impetus for maintaining high welfare standards. Accordingly, the importance of empirical research into the welfare and husbandry of captive fishes is increasingly acknowledged in both science and aquaculture, alongside growing public and governmental interest. Physical enrichment can have an important influence on welfare in of captive fishes, but many questions remain. Here, we summarise the current state of research and outline knowledge gaps in the area of physical enrichment, which is a fundamental aspect to improving welfare of captive fishes. To explore the level of research interest this area across time we conducted a series of surveys, using the number of papers published per year as a metric. These surveys highlight that work on fish welfare, while representing a relatively low proportion of fish research overall, is increasing rapidly. For species that are of aquaculture importance or used commonly as laboratory subjects, we show a positive relationship between general research interest and number of welfare‐related papers. However, for many, particularly relatively less studied, species the proportion of papers on enrichment remains low, with a slower increase compared to welfare‐related papers in general. In terms of common metrics used to quantify fish welfare, there is a reliance on growth and behaviour, with scope for inclusion and combination of a more comprehensive range of reproducible measures. We finish by highlighting recent progress, promising areas for future research and suggestions for advances in this area.