•We present a review of GHG reduction measures and their potential in shipping.•We find a large variability in CO2 reduction potential for reported measures.•CO2 emissions can be reduced by a factor 4–6 per freight unit transported.•Sector-wide reductions are impeded by expected growth in maritime transport.•Significant reductions require a combination of many individual reduction measures. CO2 emissions from maritime transport represent around 3% of total annual anthropogenic greenhouse gas (GHG) emissions. These emissions are assumed to increase by 150–250% in 2050 in business-as-usual scenarios with a tripling of world trade, while achieving a 1.5–2°C climate target requires net zero GHG emissions across all economic sectors. Consequentially, the maritime sector is facing the challenge to significantly reduce its GHG emissions as contribution to the international ambition to limit the effects of climate change. This article presents the results of a review of around 150 studies, to provide a comprehensive overview of the CO2 emissions reduction potentials and measures published in literature. It aims to identify the most promising areas, i.e. technologies and operational practices, and quantify the combined mitigation potential. Results show a significant variation in reported CO2 reduction potentials across reviewed studies. In addition, no single measure is sufficient to achieve meaningful GHG reductions. Emissions can be reduced by more than 75%, based on current technologies and by 2050, through a combination of measures if policies and regulations are focused on achieving these reductions. In terms of emissions per freight unit transported, it is possible to reduce emissions by a factor of 4–6.