In the age of Big Data and machine learning, with its ever-expanding possibilities for data mining, the question of who is entitled to control the data and benefit from insights that can be derived from them matters greatly for the shape of the future economy. Therefore, this topic should be assessed under the heading of distributive justice. There are different views on who is entitled to control data, often driven by analogies between claims to data and claims to other kinds of things that are already better understood. This chapter clarifies the value of approaching the subject of control over data in terms of (a notion of moral, rather than legal) ownership. Next, drawing on the work of seventeenth-century political theorist Hugo Grotius on the freedom of the seas, and thus on possibilities of owning the high seas, I develop an account of collective ownership of collectively generated data patterns and explore several important objections. Since control over data matters enormously and is poorly understood, we should treat questions about it as genuinely open. This is a good time to bring to bear unorthodox thinking on the matter.