Real-world experience underscores the complexity of interactions among multiple drivers of climate change risk and of how multiple risks compound or cascade. However, a holistic framework for assessing such complex climate change risks has not yet been achieved. Clarity is needed regarding the interactions that generate risk, including the role of adaptation and mitigation responses. In this perspective, we present a framework for three categories of increasingly complex climate change risk that focus on interactions among the multiple drivers of risk, as well as among multiple risks. A significant innovation is recognizing that risks can arise both from potential impacts due to climate change and from responses to climate change. This approach encourages thinking that traverses sectoral and regional boundaries and links physical and socio-economic drivers of risk. Advancing climate change risk assessment in these ways is essential for more informed decision making that reduces negative climate change impacts.