As the world overheats-potentially to conditions warmer than during the three million years over which modern humans evolved-suffering from heat stress will become widespread. Fundamental questions about humans' thermal tolerance limits are pressing. Understanding heat stress as a process requires linking a network of disciplines, from human health and evolutionary theory to planetary atmospheres and economic modeling. The practical implications of heat stress are equally transdisciplinary, requiring technological, engineering, social, and political decisions to be made in the coming century. Yet relative to the importance of the issue, many of heat stress's crucial aspects, including the relationship between its underlying atmospheric drivers-temperature, moisture, and radiation-remain poorly understood. This review focuses on moist heat stress, describing a theoretical and modeling framework that enables robust prediction of the averaged properties of moist heat stress extremes and their spatial distribution in the future, and draws some implications for human and natural systems from this framework. Moist heat stress affects society; we summarize drivers of moist heat stress and assess future impacts on societal and global scales. Moist heat stress pattern scaling of climate models allows research on future heat waves, infrastructure planning, and economic productivity.