One of the key features of the contemporary data economy is the widespread circulation of data and its interoperability. Critical data scholars have analysed data repurposing practices and other factors facilitating the travelling of data. While this approach focused on flows provides great potential, in this article we argue that it tends to overlook questions of attachment and belonging. Drawing upon ethnographic fieldwork within a Danish data-linkage infrastructure, and building upon insights from archival science, we discuss the work of data practitioners enabling the repurposing of pathology samples extracted from patients for the conduct of ‘personal medicine’ – our term to discuss the so-called old-fashioned treatment of patients – towards personalised medicine. This first involves ‘getting to know’ the tissues and unpacking their previous uses and meanings, then detaching them from their original source to extract data from such tissues and making them flow towards a new container where they can be worked on and connected with other data. As data practitioners make these tissues travel, transforming them into research data, they organise the attachments of data to new agendas, persons and places. Crucially, in our case, we observe the prominence of national attachments, whereby managing tissues and data in and out of containers involves tying them to the nation to serve its interests. We thus expose how the building of data linkage infrastructures entails more than the accumulation and curation of data, but also involves crafting meanings, futures and belonging to specific communities and territories.