Hard climate policy (e.g., regulation, taxes/pricing, phaseouts) is needed to meet ambitious climate targets, but when such policy is introduced, it can sometimes trigger backlash. Backlash involves an abrupt and forceful negative reaction by a significant number of actors seeking to reverse a policy, often through extraordinary means that transgress established procedures and norms. Yet, explanations of policy backlash remain nascent and fragmented. I synthesize insights from within and beyond climate politics to argue that contested legitimacy is central to climate policy backlash, which provokes attempts toward delegitimation. I develop a conceptual pathway to explain the occurrence of climate policy backlash and generate hypotheses about how practices of delegitimation occur, and their effects. This contributes to explaining why backlash occurs, highlighting ideational factors alongside interests and institutions. Overall, I suggest the need for a contextually embedded approach to understanding the volatile dynamics of backlash, bringing political sociology into conversation with political economy.