Like other animals, fish have unique personalities that can affect their cognition and responses to environmental stressors. These individual personality differences are often referred to as “behavioural syndromes” or “stress coping styles” and can include personality traits such as boldness, shyness, aggression, exploration, locomotor activity, and sociability. For example, bolder or proactive fish may be more likely to take risks and present lower hypothalamo–pituitary–adrenal/interrenal axis reactivity as compared to shy or reactive individuals. Likewise, learning and memory differ between fish personalities. Reactive or shy individuals tend to have faster learning and better association recall with aversive stimuli, while proactive or bold individuals tend to learn more quickly when presented with appetitive incentives. However, the influence of personality on cognitive processes other than cognitive achievement in fish has been scarcely explored. Cognitive bias tests have been employed to investigate the interplay between emotion and cognition in both humans and animals. Fish present cognitive bias processes (CBP) in which fish’s interpretation of stimuli could be influenced by its current emotional state and open to environmental modulation. However, no study in fish has explored whether CBP, like in other species, can be interpreted as long-lasting traits and whether other individual characteristics may explain its variation. We hold the perspective that CBP could serve as a vulnerability factor for the onset, persistence, and recurrence of stress-related disorders. Therefore, studying fish’s CBP as a state or trait and its interactions with individual variations may be valuable in future efforts to enhance our understanding of anxiety and stress neurobiology in animal models and humans.