The COVID-19 pandemic has highlighted that leveraging medical big data can help to better predict and control outbreaks from the outset. However, there are still challenges to overcome in the 21st century to efficiently use medical big data, promote innovation and public health activities and adequately protect individuals’ privacy. The metaphor that property is a “bundle of sticks” applies equally to medical big data. Understanding medical big data in this way raises a number of questions, including: Who has the right to make money off its buying and selling, or is it inalienable? When does medical big data become sufficiently stripped of identifiers that the rights of an individual concerning the data disappear? How have different regimes such as the General Data Protection Regulation in Europe and the Health Insurance Portability and Accountability Act in the US answered these questions differently? In this chapter, we will discuss three topics: (1) privacy and data sharing, (2) informed consent, and (3) ownership.