Emission trading can take two different forms: bilateral bargaining between polluter and receptor, or a market for emission rights which organizes trading between polluters according to a given goal of emissions reduction. This chapter focuses on the latter, today called a “cap-and-trade” policy. It provides a history of this kind of trading, both in theory and practice. The idea emerged in economics during the 1960s, in a context of growing awareness of environmental issues. Rooted in the concept of externalities, it was promoted by economists in the name of the cost efficiencies it was expected to achieve. But its early reception was very cautious. Pollution was not considered to be an economic issue, and, more generally, the idea that it could be managed by incentives (market prices but also administered prices like taxes) raised moral issues. The idea really took off in the late 1970s, mainly in the United States: as industry increasingly challenged the existing regulation, policymakers began to consider it as an acceptable political compromise and set up the first experiments to gauge its feasibility. Since then, the controversies have switched from moral concerns to practical issues of implementation. Today, while cap-and-trade instruments have become a favoured way to manage climate change, and many carbon markets have been developed, the debate now focuses mainly on their practical ability to fulfil their theoretical promise, centring on their contested economic efficiency and environmental effectiveness.