Increasing both crop productivity and the tolerance of crops to abiotic and biotic stresses is a major challenge for global food security in our rapidly changing climate. For the first time, we show how the spatial variation and severity of tropospheric ozone effects on yield compare with effects of other stresses on a global scale, and discuss mitigating actions against the negative effects of ozone. We show that the sensitivity to ozone declines in the order soybean > wheat > maize > rice, with genotypic variation in response being most pronounced for soybean and rice. Based on stomatal uptake, we estimate that ozone (mean of 2010-2012) reduces global yield annually by 12.4%, 7.1%, 4.4% and 6.1% for soybean, wheat, rice and maize, respectively (the "ozone yield gaps"), adding up to 227 Tg of lost yield. Our modelling shows that the highest ozone-induced production losses for soybean are in North and South America whilst for wheat they are in India and China, for rice in parts of India, Bangladesh, China and Indonesia, and for maize in China and the United States. Crucially, we also show that the same areas are often also at risk of high losses from pests and diseases, heat stress and to a lesser extent aridity and nutrient stress. In a solution-focussed analysis of these results, we provide a crop ideotype with tolerance of multiple stresses (including ozone) and describe how ozone effects could be included in crop breeding programmes. We also discuss altered crop management approaches that could be applied to reduce ozone impacts in the shorter term. Given the severity of ozone effects on staple food crops in areas of the world that are also challenged by other stresses, we recommend increased attention to the benefits that could be gained from addressing the ozone yield gap.