The European Data Strategy, published in 2020, aims to turn the EU into a society empowered by data which captures its benefits to generate improvements in health, well-being, the environment, transparent governance, and convenient public services. This article examines the European Data Strategy, focusing on the Data Act and Data Governance Act, and situates them within broader data governance discussions. It argues that the Strategy has at its centre a tension between fostering a robust, fair data market versus scepticism towards market-based data governance mechansims, and analyses to what extent the regulatory techniques the Data Strategy proposes can address this tension.