Fish welfare is a critical issue that needs to be addressed by the rapidly growing aquaculture industry. Scientific knowledge regarding the natural behaviors of species and the conditions in which they are kept in farms is essential for improving their welfare in aquaculture. To provide a consistent overview of the welfare of farmed fish, the organization fair-fish has created the online platform fair-fish database, which gathers ethological knowledge categorized into profiles of farmed aquatic species. The WelfareChecks on this platform are profiles based on criteria that are rated based on the likelihood and potential of the species to experience a high level of welfare in aquaculture systems, together with the certainty about the findings. A score (WelfareScore) is calculated from these ratings, serving as a reference to identify knowledge gaps, assess welfare, and suggest ways to improve it. Here, we performed an in-depth analysis of the species with WelfareChecks already published in the fair-fish database based on their respective WelfareScores. In general, although just a small percentage of farmed aquatic species (~5%) have at least a 20% chance of experiencing a good level of welfare under minimal aquaculture conditions, 60% of them have at least some potential to achieve good welfare under high-standard conditions, with more than a third of the species (~37%) having at least a 20% potential. Despite that, several species exhibit a very high frequency of low chances and potential for experiencing good welfare levels under aquaculture conditions, besides a low degree of certainty based on literature reviews. Furthermore, many others show a very frequent occurrence of unclear or nonexistent knowledge in their profiles. The current welfare state is therefore poor for the majority of farmed aquatic species; yet, there is considerable potential for improvement. However, many species are very unlikely to achieve good welfare, even under high-standard conditions. Importantly, large knowledge gaps remain for an accurate assessment of the welfare of several farmed species.