Human genomics is undergoing a step change from being a predominantly research-driven activity to one driven through health care as many countries in Europe now have nascent precision medicine programmes. To maximize the value of the genomic data generated, these data will need to be shared between institutions and across countries. In recognition of this challenge, 21 European countries recently signed a declaration to transnationally share data on at least 1 million human genomes by 2022. In this Roadmap, we identify the challenges of data sharing across borders and demonstrate that European research infrastructures are well-positioned to support the rapid implementation of widespread genomic data access.