A central question in international climate policy making is how to distribute the burdens of keeping global average temperature increase to well below 2 °C above pre-industrial levels. In particular, there are four distributional issues: how to allocate the total amount of greenhouse gases that can still be emitted, who should bear the costs of mitigation, who should bear the costs of adaptation to unavoidable climate change, and who should bear the costs of residual climate damage. Regarding these distributional issues the academic literature offers a plethora of fairness principles, such as ‘polluter pays’, ‘beneficiary pays’, ‘equal per capita rights’, ‘grandfathering’, ‘ability to pay’, ‘historical responsibility’ and ‘cost effectiveness’. Remarkably, there is a theoretical gap between these principles and the central theories of distributive justice in moral and political philosophy. As a consequence, it is unclear how these principles are related, whether they can be combined or are mutually exclusive, and what the fundamental underlying values are. This paper aims to elucidate that debate. Understanding the different underlying values may facilitate bridge-building and movement in negotiation positions.