Climate change is being exacerbated by the emissions of global warming greenhouse gases (GHGs), as a consequence of economic activities associated with energy, industry, transportation, and land use. From an economic viewpoint, the Earth’s climate is a public good and pollution a negative externality; such change therefore constitutes market failure. Controlling air pollution by utilizing economic mechanisms represents an important change in environmental thinking – literally a paradigm shift away from historical command-and-control engineering systems. Today, this approach is being utilized to mitigate the emissions of GHGs, addressing the pollution externality by putting a price on carbon. There are two economic approaches to implement such a price: (1) utilizing a government-imposed price-based mechanism such as a carbon tax or (2) allowing a market to reach the price associated with a quantity-based emission constraint, commonly referred to as emissions trading. Following the quantity-based approach, an international carbon market developed as a result of the Kyoto Protocol but decreased significantly after that agreement’s first commitment period ended in 2012. Today’s carbon market is once again increasing, due to higher prices in the EU Emissions Trading Scheme (EU ETS), China’s nascent national program, and the potential for project-based credit mechanisms in the voluntary market to help achieve corporate net-zero emissions strategies. The Paris Agreement in 2015 supports such quantity-based approaches, although trading rules for market transactions under that Agreement have still not been fully resolved. This chapter discusses the structure of these emissions trading carbon markets, the theory behind their development, their historical evolution, ongoing governance challenges, and future prospects.