Climate trends over the past few decades have been fairly rapid in many agricultural regions around the world, and increases in atmospheric carbon dioxide (CO2) and ozone (O3) levels have also been ubiquitous. The virtual certainty that climate and CO2 will continue to trend in the future raises many questions related to food security, one of which is whether the aggregate productivity of global agriculture will be affected. We outline the mechanisms by which these changes affect crop yields and present estimates of past and future impacts of climate and CO2 trends. The review focuses on global scale grain productivity, notwithstanding the many other scales and outcomes of interest to food security. Over the next few decades, CO2 trends will likely increase global yields by roughly 1.8% per decade. At the same time, warming trends are likely to reduce global yields by roughly 1.5% per decade without effective adaptation, with a plausible range from roughly 0% to 4%. The upper end of this range is half of the expected 8% rate of gain from technological and management improvements over the next few decades. Many global change factors that will likely challenge yields, including higher O3 and greater rainfall intensity, are not considered in most current assessments.