Biobanking involves the assembling, curating, and distributing of samples and data. While relations between samples and data are often taken as defining properties of biobanking, several studies have pointed to the challenges in relating them in practice. This article investigates how samples and data are curated, connected, and made mobile in practice. Building on an analysis of data collected at five hospital-based biobanks in Austria, the article describes and compares biobanking in three types of biobank collections: ‘departmental collections’, ‘project-specific collections’ and ‘hospital-wide collections’. It draws attention to the invisible work going into this infrastructure and highlights the central role of visions to make samples and data travel to a different location and thus support biomedical research. It shows that while visions of future travels are often epistemologically uncertain, they are informed by social ties and relationships between the collectives involved in the curation of samples and data on the one hand and the imagined users on the other. Finally, we point to the importance that policy actors in this domain consider the aspects we identified—and, in particular, reflect the temporalities inherent in such a research infrastructure.