The European Health Data Space Regulation (EHDS) establishes a common governance framework intended to promote the use of health data for clinical care, research, innovation, and policymaking. Academic literature has increasingly focused on anticipating the social and ethical dimensions of the EHDS, but to date, no contributions have systematically reviewed these for their policy relevance. Objectives: This study set out to (a) identify ethical and social issues associated with the EHDS in the multi-disciplinary research literature, and (b) articulate policy recommendations. Methods: A rapid review of the research literature was performed. Results: Seven overarching topics were identified. Most issues relate to secondary use of health data, with disproportionate impacts on member states already facing digitalization challenges. Discussion: We suggest that responsible governance hinges on recognition of different and at-times competing goals, interests, and requirements. A fair, just, or equitable EHDS cannot be understood strictly in terms of fair outcomes in data use, but also requires grappling with contested notions of value. Conclusion: The EHDS’s broader geopolitical significance should be emphasized. This especially includes attending to how local and regional socio-economic goals impact on what comes to be recognized as a priority in data-intensive health systems.