Cap and trade programs have been a commonly proposed method to regulate emissions of various pollutants. As many countries move forward with plans to regulate CO2 emissions, concerns over containing the costs of such policies often arise given the relatively large scope of the programs. We review three cost containment mechanisms most commonly employed in existing cap and trade policies and/or discussed in the literature: banking and borrowing, hybrid policies, and emission offsets. For each of these mechanisms we discuss the theoretical basis for the policy, potential unintended consequences and, where applicable, the effectiveness of the policy as it has been used in practice.