In the wake of the Paris Agreement, countries have yet to embark on deep decarbonisation pathways. This article explores the reasons for this limited response, taking a comparative political economy lens to identify national constraints that actively hinder climate policy progress. We discuss different metrics of climate policy progress, including emissions trends, climate legislation adoption, policy adoption, policy stringency, and policy outcomes. We then review literatures that explain varying national outcomes along these dimensions. Identified constraints include (but are not limited to) exposure to fossil fuel extraction activities, supply-side coal dependency, a lack of democratic norms, exposure to corruption, a lack of public climate awareness, and low levels of social trust. Correlation and principal component analysis of these variables demonstrates strong co-dependencies, including a North-South divide in institutional quality, trust and climate awareness that limits full participation in climate legislation and the removal of fossil subsidies. Recent trends indicate stability in corruption across the whole sample, and the continued durability of autocratic and extractivist states. We identify common constraints for five distinct country groups using cluster analysis: ‘oil & gas states’, ‘fragile states’, ‘coal-dependent development’, ‘fractured democracies’ and ‘wealthy OECD’. We highlight the need to scrutinise architectures of constraint – combinations of political economic factors that are mutually reinforcing and highly resistant to intervention.