European Health Data Spaces, national digital health records archives and similar initiatives aim to provide a mixture of legal and technical frameworks to make privacy-sensitive medical data available for data mining. The ultimate goal is to access the yet behind legal barriers hidden healthcare data treasure in order to train prognostic models for personalized medicine - from disease management to individualized drug repurposing prediction. The biggest roadblock is the GDPR. In the talk, we will discuss federated learning technology that - coupled to other privacy-enhancing technologies - allows for a secure multi-center data mining collaboration. Specifically, we will demonstrate that it does provide as accurate results as centralized solutions. We will discuss concrete applications for multi-centric genome-wide association studies, for meta-genomics, transcriptomics and proteomics analysis including batch effect correction, and for survival time analysis. One application involved >1,000 hospitals in North America, another one involves >100,000 European screening participants. Finally, we discuss the limitations and future prospects of federated learning in biomedicine and healthcare data mining.