Individual differences in cognitive abilities have been thoroughly investigated in humans and to a lesser extent in other mammals. Despite the growing interest in studying cognition in other taxonomic groups, data on individual differences are scarce for non-mammalian species. Here, we review the literature on individual differences in cognitive abilities in teleost fishes. Relatively few studies have directly addressed this topic and have provided evidence of consistent and heritable individual variation in cognitive abilities in fish. We found much more evidence of individual cognitive differences in other research areas, namely sex differences, personality differences, cerebral lateralisation and comparison between populations. Altogether, these studies suggest that individual differences in cognition are as common in fish as in warm–blooded vertebrates. Based on the example of research on mammals, we suggest directions for future investigation in fish.