Shifting our fossil-fuelled civilisation to clean modes of production and consumption requires deep transformations in our energy and economic systems. Innovation in physical technologies and social behaviours is key to this transformation. But innovation has not been at the heart of economic models of climate change. This chapter reviews the state of the art on the economics of innovation, applying recent insights to climate change. The core insight is that technological innovation is a path-dependent process in which history and expectations matter greatly in determining eventual outcomes. This insight has six important implications for climate policy design. First, efficient climate policy requires direct research subsidies for inducing and/or diffusing clean innovations, combined with carbon pricing (whether by taxes or trading). Second, both public and private sector involvement is required. Third, path dependence and system inertia imply that delaying policies that redirect innovation towards clean technologies significantly increases costs in the future. Fourth, more developed countries should act as leaders in clean technology and should subsidise access to such technologies for less developed countries. Fifth, if a transition from coal to clean energy is to be made via intermediates (for example, gas), the use of gas (without carbon capture) should be agreed to be on a time-limited basis. Finally, investment in coal should not be encouraged, as its continued use is only safe if we assume the cost-effectiveness of carbon capture and storage (CCS) technologies. While much greater efforts should be taken to reduce the costs of CCS, the speed that these technologies can be developed and deployed is uncertain.