Carbon budgets, which define the total allowable CO2 emissions associated with a given global climate target, are a useful way of framing the climate mitigation challenge. In this paper, we review the geophysical basis for the idea of a carbon budget, showing how this concept emerges from a linear climate response to cumulative CO2 emissions. We then discuss the difference between a “CO2-only carbon budget” associated with a given level of CO2-induced warming and an “effective carbon budget” associated with a given level of warming caused by all human emissions. We present estimates for the CO2-only and effective carbon budgets for 1.5 and 2 °C, based on both model simulations and updated observational data. Finally, we discuss the key cont...