This paper considers potential implications for international shipping by deriving two global CO2 budgets that are consistent with a 50% chance of limiting global warming to 2°C and 1.5°C, respectively and translating the global CO2 budgets to CO2 budgets for international shipping, assuming that a fair sharing of mitigation efforts suggests international shipping cut its emissions by the same proportion that is required for the global average1. It also explores what reductions in the CO2 intensity (and, in particular, shipping’s Energy Efficiency Operational Indicator, EEOI) of maritime transport are needed to keep within these CO2 budgets against the backdrop of continued growth in the shipping industry and projected rises in demand for sea transport and reviews the evidence from recent studies of the trends and drivers of trends in the shipping sector’s CO2 intensity.