Emissions trading systems and carbon taxes are two market-based policy instruments for responding to the climate change externality. This article focuses on the relationship between the design of these carbon pricing instruments and business cycle fluctuations. In particular, whether and how these instruments should respond to business cycles is a topical policy question. To answer it, the article brings together the relevant empirical and theoretical results from the academic literature. It finds that building responsiveness into the design of carbon pricing instruments can reduce the burden of regulation by distributing it more evenly over time. Specifically, relative to a fixed cap emissions trading system, this can be achieved by relaxing the cap during economic expansions and tightening it during recessions. Similarly, a carbon tax regime in which the tax is higher during expansions, and lower during recessions, is likely to improve welfare compared to a cyclically unresponsive tax. In practice, a mechanism which renders real-world carbon pricing instruments responsive is a challenging task. The article provides an overview of the trade-offs involved by focusing on the broad classes of mechanisms explored in the literature. The choice of responsiveness-inducing mechanism must crucially consider country characteristics such as the properties of fluctuations in the country's GDP and emissions, any relevant political economy concerns and its institutional background.