The growth of big data and the development of digital data infrastructures raises numerous questions about the nature of data, how they are being produced, organized, analyzed and employed, and how best to make sense of them and the work they do. Critical data studies endeavours to answer such questions. This paper sets out a vision for critical data studies, building on the initial provocations of Dalton and Thatcher (2014). It is divided into three sections. The first details the recent step change in the production and employment of data and how data and databases are being reconceptualised. The second forwards the notion of a data assemblage that encompasses all of the technological, political, social and economic apparatuses and elements that constitutes and frames the generation, circulation and deployment of data. Drawing on the ideas of Michel Foucault and Ian Hacking it is posited that one way to enact critical data studies is to chart and unpack data assemblages. The third starts to unpack some the ways that data assemblages do work in the world with respect to dataveillance and the erosion of privacy, profiling and social sorting, anticipatory governance, and secondary uses and control creep. The paper concludes by arguing for greater conceptual work and empirical research to underpin and flesh out critical data studies.