This article describes the emergent and unstable dispositif of climate finance that is being built from iterative experiments in climate finance provision. The article provides a periodisation of different phases of climate finance from the 1990s onward using examples from REDD+, ecosystem services, the Green Climate Fund, green bonds, and insurance‐based derivatives, and connects this periodisation to broader processes of financialisation. It analyses how climate finance projects incorporate competing systems of accounting denominated in carbon, natural capital, “green‐ness”, insurance risk and internationally transferred mitigation outcomes. The article argues that many accounting units are evident in current climate finance products, each loosely derived from a different phase in this periodisation. However, experiments in calculating time and value in climate finance continue, and although risk is being increasingly used to correlate different denominators of value, an overall solution for how climate change is to be accounted for in financial interventions remains elusive.