Carbon markets have developed into an international market mechanism based on the agreements reached at COP26 in Glasgow in 2021. Carbon market development and the agreement at COP26 are not without their problems. Examining the history of the development of the agreement reveals many issues which are still relevant today. The main issues include the capacity of the market to deliver large-scale and rapid fossil fuel emissions reductions, the integrity of the accounting framework, potential impacts on biodiversity and natural capital and risks around the delivery of co-benefits and the failure of robust mechanisms for the rights of Indigenous people. The most pressing issue is that the agreed market mechanism will not deliver a rapid reduction in fossil fuel emissions. Hope exists in that Nationally Determined Contribution (NDCs) and the transparency around the carbon markets process can be strong enough to reduce the risks of carbon market failure. There are principles that can be applied to carbon trading and emissions reductions. The carbon integrity movement can adopt such principles and guide the carbon market. The carbon market mechanism in place cannot deliver required emissions reductions unless carbon integrity principles are adopted.