In some food production systems, sustainability and acceptability are considered umbrella concepts that can be assessed through a combination of criteria and indicators. After a remarkable and somewhat chaotic development in the early ‘90s, European aquaculture has been evolving in both scientific and policy domains to improve, and to prove, its sustainability. The updated review of the literature and policy framework presented in this contribution highlights gaps in European studies, addressing mostly concerns over the environmental impacts and food safety and less in terms of economic impacts on other coastal activities or the effects on social values and local traditions. The analysis of the legislative framework demonstrates that the existing legislation adopted at different levels addresses most of the criteria of social acceptability through binding rules and supporting guidelines. Nonetheless, some elements of social concerns, such as the impact of escapes or the degradation of the landscape, remain unaddressed. A number of actions are proposed that should be implemented by all the actors involved in aquaculture management to improve social attitudes and thus, the acceptance by the different segments of the society.