Since the ratification of the Kyoto Protocol by a large number of countries, carbon trading has been expanding continuously. The objective of this chapter is to study the trading of Kyoto credits. We begin with the origins of carbon trading in order to understand how carbon trading works in Europe and specifically the functioning of the European Union Emission Trading Scheme (EU ETS). This scheme has facilitated the creation of several spot, futures and options markets where it is possible to trade European Union Allowances (EUAs). The different types of contracts that permit the trading of EUAs are analysed in detail. Additionally, as one of the objectives of the third flexibility mechanism of the Kyoto Protocol (emissions trading) is the creation of a global carbon market, the possibilities of linking the EU ETS with the other United Nations carbon markets are also studied. Finally, the trading of the units generated by the Joint Implementation and the Clean Development Mechanism is also explored. The main conclusion of the chapter is that the EU ETS has succeeded in imposing a price on carbon emissions, which was one of its most important objectives.