In 2020, the European Union set the goal to become a leading role model for a society empowered by data to make better decisions––in business and the public sector. This Article analyzes the European strategy for data (‘Data Strategy’) and its two main regulatory elements, the Data Governance Act and the Data Act, and situates them within the wider academic discussion on data governance. To the best of our knowledge, this has not been done yet in the literature. We argue that the Data Strategy has at its center a tension between creating market-based mechanisms for data sharing on the one hand, and on the other hand respecting data subjects’ privacy rights and promoting alternative data governance mechanisms. We analyze to what extent the regulatory techniques the Data Strategy proposes are able to address this tension.