While there is a clear need to apply data analytics in the healthcare sector, this is often difficult because it requires combining sensitive data from multiple data sources. In this paper, we show how the cryptographic technique of secure multi-party computation can enable such data analytics by performing analytics without the need to share the underlying data. We discuss the issue of compliance to European privacy legislation; report on three pilots bringing these techniques closer to practice; and discuss the main challenges ahead to make fully privacy-preserving data analytics in the medical sector commonplace.