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 contributors to uncertainty in carbon budget estimates and suggest some implications of this uncertainty for decision-making. Based on the analysis presented here, we argue that while the CO2-only carbon budget is a robust upper bound on allowable emissions for a given climate target, the size of the effective carbon budget is dependent on the how quickly we are able to mitigate non-CO2 greenhouse gas and aerosol emissions. This suggests that climate mitigation efforts could benefit from being responsive to a changing effective carbon budget over time, as well as to potential new information that could narrow uncertainty associated with the climate response to CO2 emissions.