The era of big data opens up new opportunities in personalised medicine, preventive care, chronic disease management and in telemonitoring and managing of patients with implanted devices. The rich data accumulating within online services and internet companies provide a microscope to study human behaviour at scale, and to ask completely new questions about the interplay between behavioural patterns and health. In this paper, we shed light on a particular aspect of data-driven healthcare: autonomous decision-making. We first look at three examples where we can expect data-driven decisions to be taken autonomously by technology, with no or limited human intervention. We then discuss some of the technical and practical challenges that can be expected, and sketch the research agenda to address them.