Climate change, population growth and socio-structural changes will make meeting future food demands extremely challenging. As wheat is a globally traded food commodity central to the food security of many nations, this paper uses it as an example to explore the impact of climate change on global food supply and quantify the resulting greenhouse gas emissions. Published data on projected wheat production is used to analyse how global production can be increased to match projected demand. The results show that the largest projected wheat demand increases are in areas most likely to suffer severe climate change impacts, but that global demand could be met if northern hemisphere producers exploit climate change benefits to increase production and narrow their yield gaps. Life cycle assessment of different climate change scenarios shows that in the case of one of the most important wheat producers (the UK) it may be possible to improve yields with an increase of only 0.6% in the emission intensity per unit of wheat produced in a 2. °C scenario. However, UK production would need to rise substantially, increasing total UK wheat production emissions by 26%. This demonstrates how national emission inventories and associated targets do not incentivise minimisation of global greenhouse gas emissions while meeting increased food demands, highlighting a triad of challenges: meeting the rising demand for food, adapting to climate change and reducing emissions.