More than one billion people have today insufficient food to sustain life and food supply needs to double by 2050 to meet this demand. The most serious challenges societies will face over the next decades include providing food and the water needed for food production, to a world that will see its population increase by a third in the face of mounting environmental stresses, worsened by the consequences of Global Climate Change (GCC). The challenge of increasing food production will be greatest for the production of the staple grain crops. Heat tolerance of crops varies greatly and wheat, which provides 20% of all protein and 19% of all calories for human consumption, is among major staples most sensitive. GCC will have a major impact on crop production, both positive and negative, but in low latitudes, where most developing countries are located, impact of GCC on wheat production is likely to be very severe. There are many estimates regarding the impact of GCC on wheat yield and they congregate around yield losses between 20% and 30% by 2050 in developing countries with an assumed temperature increase of 2 to 3°C, if no mitigating measures are taken. Public wheat breeding efforts have focused in recent decades on increasing resistance to disease and abiotic stress and quality, while efforts to raise genetic yield potential per se have received scant attention. The fundamental bottleneck to raising productivity, namely radiation use efficiency, has barely changed since wheat breeding began and need to be addressed urgently. The challenge is to develop technologies (varieties, agronomic practices, etc.) that not only compensate the negative impact of GCC but have a 70% higher yield potential than in 2010, with more effective use of light, irrigation water and nutrients. Even without GCC this is a formidable challenge.