Aquaculture has the potential to support a sustainable and equitable food system in line with the United Nations Sustainable Development Goals (SDG) on food security, climate change, and biodiversity (FCB). Biological diversity amongst aquaculture organisms can drive diverse contributions to such goals. Existing studies have assessed the performance of a limited number of taxa in the general context of improving aquaculture production, but few explicitly consider the biological attributes of farmed aquatic taxa at the FCB nexus. Through a systematic literature review, we identify key traits associated with FCB and evaluate the potential of aquaculture to contribute to FCB goals using a fuzzy logic model. The majority of identified traits are associated with food security, and two-thirds of traits linked with food security are also associated with climate change or biodiversity, revealing potential co-benefits of optimizing a single trait. Correlations between FCB indices further suggest that challenges and opportunities in aquaculture are intertwined across FCB goals, but low mean FCB scores suggest that the focus of aquaculture research and development on food production is insufficient to address food security, much less climate or biodiversity issues. As expected, production-maximizing traits (absolute fecundity, the von Bertalanffy growth function coefficient K, macronutrient density, maximum size, and trophic level as a proxy for feed efficiency) highly influence a species’ FCB potential, but so do species preferences for environmental conditions (tolerance to phosphates, nitrates, and pH levels, as well as latitudinal and geographic ranges). Many highly farmed species that are typically associated with food security, especially finfish, score poorly for food, climate, and biodiversity potential. Algae and mollusc species tend to perform well across FCB indices, revealing the importance of non-fish species in achieving FCB goals and potential synergies in integrated multi-trophic aquaculture systems. Overall, this study provides decision-makers with a biologically informed assessment of desirable aquaculture traits and species while illuminating possible strategies to increase support for FCB goals. Our findings can be used as a foundation for studying the socio-economic opportunities and barriers for aquaculture transitions to develop equitable pathways toward FCB-positive aquaculture across nuanced regional contexts.