Climate trends over the past few decades have been fairly rapid in many agricultural regions around the world, and increases in atmospheric carbon dioxide (CO 2 ) and ozone (O 3 ) levels have also been ubiquitous. The virtual certainty that climate and CO 2 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 CO 2 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, CO 2 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 O 3 and greater rainfall intensity, are not considered in most current assessments.Many factors will shape global food security over the next few decades, including changes in rates of human population growth, income growth and distribution, dietary preferences, disease incidence, increased demand for land and water resources for other uses (i.e. bioenergy production, carbon sequestration, and urban development), and rates of improvement in agricultural productivity. This latter factor, which we define here simply as crop yield (i.e., metric tons of grain production per hectare of land), is a particular emphasis of the plant science community, as researchers and farmers seek to sustain the impressive historical gains associated with improved genetics and agronomic management of major food crops.Sources of growth in agricultural productivity are also multifaceted and include levels of funding for public and private research and development, changes in soil quality, availability and cost of mineral fertilizers, atmospheric concentrations of CO 2 and ozone (O 3 ), and changes in temperature (T) and precipitation (P) conditions. This Update focuses on changes in weather, CO 2 , and O 3 in agricultural areas and how that has affected and will affect crop productivity. In doing so, we recognize that this is only part of the fuller story on crop productivity, which in turn is only part of the fuller story on future food security. For example, this Update is silent on the many ways that global change can influence food security via pathways other than agricultural productivity, such as by influencing human disease incidence or income growth rates.The main question of interest here is the following: how important will climate change and CO 2 be in shaping future crop yields at the global scale, relative to the many other factors that i...