While most animals have received increasing attention for their welfare, consideration for fish welfare has started more recently, particularly since the recognition that fish have emotions and complex cognitive abilities. Housing conditions in fish farms do not always meet fish ethological requirements as these conditions lack sufficient sensory and cognitive stimulations. An approach to address this issue involves enriching the rearing environment by including social, food, physical, or cognitive stimuli. Cognitive enrichment (CE) is a recent but promising concept to improve fish welfare by manipulating the predictability and controllability of their environment. It relies not only on the ability of fish to predict positive and negative events but also on their ability to perform and succeed in operant conditioning. In our present review, we identified four categories of CE: (i) feeding predictability, (ii) predictability of a negative event, (iii) operant conditioning through self-feeders, and (iv) learning experiences. Existing CEs were reviewed for their effects on behaviour, brain, zootechnical performances, and welfare in terms of physiological stress or physical integrity in the aquarium and farmed teleost fish. The review highlights unbalanced categories and the lack of adequate multidisciplinary analyses to assess the effects of these categories on fish welfare. Providing free access to self-feeders seems to be a good strategy, given its positive effects on zootechnical and physiological parameters. Other categories showed contradictory and species-dependent results; hence, further studies are required to confirm the benefits of CE on fish welfare. Finally, further investigations should also validate current CE systems and assess other strategies that may trigger positive emotions in fish.