International organisations (IOs) often serve as the ‘engine room’ of ideas for structural reforms at the national level, but how do IOs construct cognitive authority over the forms, processes and prescriptions for institutional change in their member states? Exploring the analytic institutions created by IOs provides insights into how they make their member states ‘legible’ and how greater legibility enables them to construct cognitive authority in specific policy areas, which, in turn, enhances their capacity to influence changes in national frameworks for economic and social governance. Studying the indirect influence that IOs can exert over the design of national policies has, until recently, often been neglected in accounts of the contemporary roles that IOs play and the evolution of global economic governance. By ‘seeing like an IO’, we can increase our understanding of the cognitive and organisational environment that guides an IO's actions and informs its policy advice to states, which enables a more comprehensive picture of how the everyday business of global governance works in practice. Instead of ‘black boxing’ IOs, the contributors to this special issue demonstrate how studying IOs from the inside out expands our understanding both of the policy dialogue between IOs and their member states and how IOs and states learn from each other over time.