Research infrastructures such as biobanks are increasingly important for science and society. This paper focuses on the transition of biobanks from being a research tool of individual research groups to complex, internationally networked research infrastructures supporting large-scale biomedical investigations, and the challenges that this change poses for governance in relation to management, funding, ethical and legal issues. A major problem for most publicly funded biobanks is that funding remains time-limited and is normally associated with specific research projects. Yet, as biobanks are becoming large research infrastructures, they are requiring new forms of sustainable funding. Based on ten in-depth case studies with biobanks of different sizes from different EU countries, we conclude that the growth in scale triggers the need for different governance structures, based on the specialization and professionalization of technical tasks, the formalization of many management practices and a shift in funding structures.