This article reflects on what doing critical policy sociology means in shifting theoretical, empirical and methodological contexts of education. We focus our analytical lens on two primary considerations. First, we reflect on the "politics of criticality," examining differing claims and debates about what it means to do critical research and be a critical researcher of education policy, paying particular attention to how critical policy sociologists position their work in relation to elite power and policy networks. Second, we build on these foundations to consider the trend towards researching mobilities within critical policy sociology, arguing that contemporary 'follow the policy' research risks orienting researchers to the problems and agendas already established by elite policy agents and organisations, while obscuring the not-so-mobile forces that continue to define education policy and practice. We also raise questions about the elite networks and privileged levels of resourcing typically required to conduct this kind of research. In conclusion, we invite further discussion on the politics of knowledge production and challenges for policy sociologists seeking to be critical in shifting contexts.