Carbon pricing has been adopted as a key climate policy measure in an increasing number of jurisdictions. With much of the world moving towards net-zero targets since the entry into force of the Paris Agreement, carbon pricing instruments now operate in a different context for climate policy than when economists first proposed them. This report re-examines the theory of diverse models of carbon pricing, especially for industrial decarbonisation, where concerns about carbon leakage risk and competitiveness play an important role in the policy debate. The report reviews implications for the effectiveness of climate policy and the need to reach climate neutrality in other regions when adopting measures to mitigate the risk of carbon leakage. It then discusses the concept of climate clubs and the potential for more inclusive ways of cooperating on climate policy beyond just carbon pricing.