World population, now 7.55 billion people, will increase to 9.4-10.2 billion in 2050 and 9.6-13.2 billion in 2100. Global food demand in 2050 is projected to increase by at least 60% above 2006 levels to meet the world's food needs for growing populations. Maize, wheat and rice are the main grain crops in the world, accounting together for approximately 90% of global cereal crop yields. Over the last six decades, global mean surface temperature increased at a rate of 0.12℃ per decade. Relative to the period of 1986-2005, global surface temperature is projected to increase 1-3.7℃ in the late 21st century. Climate warming has led to a reduction of grain crop yields. The sensitivity of maize to climate warming is more pronounced than that of wheat. Global yields of maize and wheat decreased by 3%-12% and 3%-9% for 1℃ warming, respectively. Warming is likely beneficial to rice production in mid- and high-latitudes, but leads to loss of rice yield in low-latitude. Yield losses induced by climate warming are greater in tropical regions than in temperate regions, with the loss of 5%-12% per degree warming for tropical maize and wheat and less than 5% for temperate maize and wheat. Crop yields are more sensitive to climate warming in rain-fed agriculture than in irrigated agriculture. Irrigation can effectively reduce the negative impact of warming on crop yield. Response of crop yields to climate warming is nonlinear. The sensitivity of crop yield to climate warming is further enhanced with increasing temperature, when the temperature is above the optimum thresholds of crop growth. Elevated atmospheric CO_2 concentration could benefit crop yields by increasing photosynthesis, and thus offset the yield losses due to climate warming to some extent. The fertilization effect of rising CO_2 concentration on crop yield in the future seems optimistic from model simulations. However, there is big uncertainty in the magnitude of the CO_2 effect and the significance of interactions with other factors. A primary reason for this uncertainty is the limited availability of experimental data on CO_2 responses for crops grown under various field conditions. Moreover, no models currently account for the interactions of CO_2 with temperature, varieties, water status, and nitrogen availability. The free-air CO_2 enrichment (FACE) technique remains the best platform to test plants under the open-field conditions. The future FACE experiments should focus on the responses of crop production to various levels of elevated CO_2 and interactions with warmer temperature, water status and nitrogen input. The uncertainties in CO_2 fertilization effect could be reduced when the field experiments are largely expanded. Furthermore, improving temperature and CO_2 relationships in models is essential to precisely assess the CO_2 fertilization effect at regional and/or global scales.