The Paris Agreement recognises the heterogeneity of approaches being implemented across jurisdictions and that parties may voluntarily engage in cooperative approaches involving use of internationally transferred mitigation outcomes towards their nationally determined contributions. Many of these diverse approaches involve putting a price on carbon, usually through emissions trading schemes or carbon taxes. Engaging the private sector at scale will be crucial for these carbon pricing mechanisms to operate efficiently in bringing about behavioural changes that will accelerate mitigation of greenhouse gas emissions and generate greater investment in climate change solutions. This will only happen on the scale necessary if there are clear, well-designed and properly functioning markets for the international transfer of mitigation outcomes and for trading carbon assets more generally. Achieving this mandates the development and implementation of processes to value mitigation outcomes, that is, to assess their mitigation value, and corresponding institutional arrangements to oversee such assessment processes. Mitigation value assessments will facilitate fungibility, enabling trading of these carbon assets across jurisdictions. This paper begins with a look at how the inter-governmental negotiations are addressing this need, and analyses how the literature has approached the subject, before setting out proposals aimed at stimulating debate on what these processes and institutional arrangements might appropriately include.