With the creation of the European Health Data Space (EHDS), the EU aims to foster the exchange of patients’ health data across national borders for primary use in healthcare and secondary use for research and innovation. The draft Regulation builds on years of efforts to gradually establish and roll out secure cross-border exchange of health data, thereby boosting implementation of digital health products and services, also in hospitals. However, achieving interoperability for continuous healthcare within and across EU Member States remains challenging. In this chapter, we discuss the current state of the EHDS and its potential impacts on hospitals’ digital maturity. At this stage of the draft Regulation, these cannot be determined with certainty, but the EHDS promises to pool technological, ethical, and political advancements of over two decades and add a new component to inpatient care delivery and clinical research: the ability to access health data of patients from another EU Member State, with the patients maintaining control over such data. A certain degree of digital maturity in hospitals, particularly in the domains of cybersecurity, data management, and exchange/interoperability, is required to fully utilise the potential of the EHDS, in addition to establishing cross-organisational relationships.