Science rarely proceeds beyond what scientists can observe and measure, and sometimes what can be observed proceeds far ahead of scientific understanding. The twenty-first century offers such a moment in the study of human societies. A vastly larger share of behaviours is observed today than would have been imaginable at the close of the twentieth century. Our interpersonal communication, our movements and many of our everyday actions, are all potentially accessible for scientific research; sometimes through purposive instrumentation for scientific objectives (for example, satellite imagery), but far more often these objectives are, literally, an afterthought (for example, Twitter data streams). Here we evaluate the potential of this massive instrumentation-the creation of techniques for the structured representation and quantification-of human behaviour through the lens of scientific measurement and its principles. In particular, we focus on the question of how we extract scientific meaning from data that often were not created for such purposes. These data present conceptual, computational and ethical challenges that require a rejuvenation of our scientific theories to keep up with the rapidly changing social realities and our capacities to capture them. We require, in other words, new approaches to manage, use and analyse data.