This working paper commissioned by the World Bank Carbon Markets and Innovation Practice (GCCMI) critically examines experience with carbon markets under the Kyoto protocol. The de facto end of the Kyoto Protocol and heralding of the Paris Agreement era has created the space for critical evaluation of trading carbon assets. The Kyoto Protocol and Paris Agreement diverge markedly in scope, centralization, and logic. As a result, the Article 6 carbon market mechanisms that emerge under Paris are likely to be very different to those that emerged under Kyoto. Nonetheless, experience with carbon markets under the Kyoto Protocol remains informative. This paper argues that there is still an economic and political rationale for trading carbon assets across borders. Trade in carbon assets can help reduce the costs of mitigation and facilitate emissions abatement at least-cost locations. When designed well, carbon market mechanisms can also facilitate learning, mobilize the private sector, and encourage transparency of mitigation efforts. Crucially, carbon markets could help support the operating logic of the Paris Agreement by binding signatories together and enhancing collective ambition. However, done badly, linking emissions systems could entail some risks to environmental integrity. In addition, given continued delays to the clarification of Article 6 and the need for strong action now, countries should not wait to implement effective domestic mitigation instruments such as carbon.