Advocates of Big Data assert that we are in the midst of an epistemological revolution, promising the displacement of the modernist methodological hegemony of causal analysis and theory generation. It is alleged that the growing ‘deluge’ of digitally generated data, and the development of computational algorithms to analyse them, has enabled new inductive ways of accessing everyday relational interactions through their ‘datafication’. This paper critically engages with these discourses of Big Data and complexity, particularly as they operate in the discipline of International Relations, where it is alleged that Big Data approaches have the potential for developing self-governing societal capacities for resilience and adaptation through the real-time reflexive awareness and management of risks and problems as they arise. The epistemological and ontological assumptions underpinning Big Data are then analysed to suggest that critical and posthumanist approaches have come of age through these discourses, enabling process-based and relational understandings to be translated into policy and governance practices. The paper thus raises some questions for the development of critical approaches to new posthuman forms of governance and knowledge production.