This paper addresses the evolution of maritime transport demand in response to global climate change mitigation and adaptation efforts. The complexity of the global shipping system makes predicting volumes and patterns of long-term future international maritime trade a challenging task which is best explored by building scenarios rather than ‘precise’ forecasts. We present four contrasting scenarios of international maritime trade out to 2050, available in high resolution in terms of the dimensions studied (regions, countries, commodities, decades), which are consistent with high and low levels of global CO2 mitigation and associated climate impacts. The scenarios project trade increasing to between two and four times the 2010 value by 2050. Scenarios characterised by low temperature increases and material intensity lead to the lower bound trade increase with high trade growth in bioenergy commodities. Unfettered production growth across countries, high temperature increases and material intensity lead to a quadrupling of trade across energy, containerised, dry and wet commodities. The estimated range is lower than those in existing scenarios and forecasts in which globalisation is assumed to continue apace. The scenarios which project the highest growth presupposes both limited decarbonisation (in contrast to the Paris Agreement) and continued growth in expanding markets. The scenarios therefore become a valuable policy and decision-making tool to address technological and operational change required of the shipping sector, if it is to deliver mitigation in line with the Paris Agreement.