This paper focuses on the yield prospects of wheat, rice and maize since these cereals dominate human diet, and since continued yield growth is considered the major route to meeting future global demand for food, feed and fuel. We define for a region farm yield (FY), attainable yield (AY, as reached with the best technology and prudent economics), and potential yield (PY, yield with the best varieties and agronomy and no manageable biotic or abiotic stresses). FY progress is a function of progress in PY and in closing the gap between PY and FY (we express this gap as a % of FY). Globally wheat and rice annual yield increases (as a % of current yield) are falling and are now just below 1%, while that for maize is 1.6%. For rice and wheat, the growth of yields in absolute terms (kg/ha/year) are also falling in developing countries. Global demand modelling to 2050 predicts large real price sensitivity to yield growth rates, with significant price increases if current rates cannot be increased. FY, PY and yield gaps are examined in more than 20 important “breadbasket” regions around the world. For wheat annual PY progress currently averages about 0.5%, and the yield gap 40% (range 25 to 50%), while for rice PY growth is also about 0.5% while the yield gap averages 75% (range 15 to 110%). Maize is distinctive with a current average PY growth of around 1% and a yield gap which ranges from around 30% (Iowa, some uncertainty with PY) to over 200% (sub Saharan Africa). A yield gap of 25% or less probably implies that FY is approaching attainable yields, AY. Yield gaps tend to be larger in developing countries, and seem to be closing only slowly except in the case of maize in Iowa and major cereals in Egypt. Prospects for yield gap closing are discussed. A multitude of constraints can reduce FY, ranging from infrastructural and institutional ones bearing upon farm gate costs and prices and farmer skills and attitudes, to diverse technical constraints. The resolution of the latter in turn depends largely on agronomic and breeding interventions (e.g., better resistance to biotic stresses), though these must be resolved in concert with the other constraints if they are to have significant impact in resource-poor farmers’ fields. Yield gap closing must be a priority for maize in sub Saharan Africa. Prospects for PY increase are discussed. PY gain is increasingly related to greater biomass production, implying greater efficiency of utilization of solar radiation. Recent progress appears to have raised this efficiency, while the theoretical limit still appears to leave scope for further increase. In addition PY in water-limited situations (PYw) will depend on further harvest index increase. In rice and wheat heterosis offers prospects for yield gain. We remain sceptical of the medium term prospects of genetic modification (GM) for yield per se, especially PY, but recognize that existing GM crops often deliver higher yields because of gap closing benefits (such as reduced pest losses). New molecular tools for selection show promise for increasing breeding efficiency, but the marginal cost of yield gains is likely to rise. Strong private investment in breeding, as seen with maize, could play a bigger global role, accompanied by facilitating policies. . We recognize in addition the importance of input efficiency and total factor productivity (TFP) for determining real prices, while prices of non-renewables (energy for traction and N fertilizer; phosphorus) are a relevant concern. TFP in agriculture continues to grow, and many examples confirm the general synergy amongst modern input technologies that achieve not only greater yield but also greater resource use efficiency (e.g., N, P, water, fuel, labour). There are also large gaps in input use efficiency that offer much scope for improved crop and resource management to deliver more with less. Investments in R&D, farmers’ information and skills, and good policy drive this process, and will determine future success or failure.