Abstract By 2050, the world population is likely to be 9.1 billion, the CO2 concentration 550 ppm, the ozone concentration 60 ppb and the climate warmer by ca 2°C. In these conditions, what contribution can increased crop yield make to feeding the world? CO2 enrichment is likely to increase yields of most crops by approximately 13 per cent but leave yields of C4 crops unchanged. It will tend to reduce water consumption by all crops, but this effect will be approximately cancelled out by the effect of the increased temperature on evaporation rates. In many places increased temperature will provide opportunities to manipulate agronomy to improve crop performance. Ozone concentration increases will decrease yields by 5 per cent or more. Plant breeders will probably be able to increase yields considerably in the CO2-enriched environment of the future, and most weeds and airborne pests and diseases should remain controllable, so long as policy changes do not remove too many types of crop-protection chemicals. However, soil-borne pathogens are likely to be an increasing problem when warmer weather will increase their multiplication rates; control is likely to need a transgenic approach to breeding for resistance. There is a large gap between achievable yields and those delivered by farmers, even in the most efficient agricultural systems. A gap is inevitable, but there are large differences between farmers, even between those who have used the same resources. If this gap is closed and accompanied by improvements in potential yields then there is a good prospect that crop production will increase by approximately 50 per cent or more by 2050 without extra land. However, the demands for land to produce bio-energy have not been factored into these calculations.