Central clearing counterparties (CCPs) have a variety of economic rationales. The Great Recession of 2007–2009 led regulators to mandate CCPs for most interest-rate and credit derivatives, markets in which large amounts of risks are transferred across agents. This change led to a large increase in CCP studies, which along with classical studies are surveyed in this article. For example, multilateral netting, the insurance against counterparty risk, the effect of CCPs on asset prices and fire sales, margins setting, the default waterfall, and CCP governance are discussed here. We review both CCP theory and empirical work and conclude by discussing regulatory issues. Expected final online publication date for the Annual Review of Financial Economics, Volume 13 is March 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.