The creation of the European health data space is one of the core actions promoted by the European Commission in its EU Data Strategy. This task is challenging due to technical, organisational, economic issues that require different measures. This paper focuses on the issues in the legal field and identifies four key legal areas where the creation of a European health data space may face obstacles. These areas are: 1) rules on the provision of healthcare in the Member States; 2) protection of personal data in healthcare provision and medical research; 3) control and use of non-personal data and 4) the regulatory framework on AI. The article analyses and compares these areas and provides a systemised view on causes and consequences. The article concludes with an outlook further legislatives developments related to the European health data space.