Recent years have seen a ‘wave’ of national climate assemblies, which bring together randomly-selected citizens to deliberate and make recommendations on aspects of the climate crisis. Assessments of the legitimacy of these interventions and their capacity to improve climate governance have focused on their internal design characteristics, but the fundamental question of how they are integrated into complex constellations of political and policy institutions is underexplored. This article constructs a framework for understanding their integrative design characteristics, drawing on recent work on ‘robust governance’. The framework is used to explore the connection of six national-level climate assemblies with political institutions, public debate and civil society. Our findings highlight immense variety in the integrative design of these climate assemblies. This variety challenges the view of assemblies as a standardised object with predictable effects on legitimacy and governance capacity, whilst also refining deliberative systems theory’s highly abstracted conceptions of integration and impact.