Knowledge of the shared resources—or commons—that aquaculture systems rely on, and the appropriate rule and norm systems to govern them—or institutions—is far behind other natural resource use sectors. In this article, we provide a conceptual framework for identifying the social and environmental commons creating collective action problems for aquaculture governance. Collective action problems, or social dilemmas, create problems for governing shared resources because the typical strategies for individual use (maximisation; free riding) are often divergent from broader group interests (e.g. fair contributions; sustainable use). This framework helps identify two types of collective action problems in aquaculture: first‐order (direct use and provision of commons) and second‐order (provision, maintenance and adaptation of institutions to govern commons). First‐order aquaculture commons with governance challenges include water quality, water quantity, physical space, inputs, genetic diversity, mitigating infectious disease, earth and climate stability, infrastructure, knowledge and money. Second‐order institutions govern the use of first‐order commons. These include rule and norm systems that structure property rights and markets, aiming to better align individual behaviour and collective interests (e.g. sustainability goals) through governance. However, which combination of institutions will fit best is likely to be unique to context, where aquaculture has important differences from capture fisheries and agriculture. We provide four case examples applying our conceptual framework to identify existing aquaculture commons, institutions and governance challenges in Peru (mariculture), the Philippines (earthen ponds), Nepal (raceways) and Denmark (recirculation).