From electronic health records to telemedicine, the digitization of healthcare in the countries of the European Union is progressing at different speeds and resembles a patchwork quilt. It is certainly true that there are a large number of promising European initiatives in the e-health sector. But a clear, pan-European vision is still lacking. In an impulse paper, we argue for an integrated e-health strategy. Such a strategy must include a European Health Data Space to promote innovation, economic growth, and optimal healthcare.