Extremely high air temperatures are uncomfortable for everyone. For some segments of the population, they can be deadly. Both the physical and societal aspects of intense heat waves in a changing climate warrant close study. The large-scale meteorological patterns leading to such events lay the framework for understanding their underlying causal mechanisms, while several methods of quantifying the combination of heat and humidity can be used to determine when these patterns result in stressful conditions. We examine four historic heat waves as case studies to illustrate differences in the structure of heat waves and the variety of effects of extreme heat on humans, which are characterized in terms of demographic, geographic, and socioeconomic impacts, including mortality and economic ramifications. Weather station data and climate model projections for the future point to an increase in the frequency and intensity of extreme heat waves as the overall climate gets warmer. Changes in the radiative energy balance of the planet are the principal culprit behind this increase. Quantifying changes in the statistics of extreme heat waves allows for examination of changes in their potential contribution to human health risk. Large-scale mortality during heat waves always occurs within a context of other factors, including public health policy, rural and urban management and planning, and cultural practices. Consequently, the impacts of heat waves can be reduced, and may in many places be manageable into the future, through implementation of such measures as public health warning systems, effective land management, penetration of air conditioning, and increased monitoring of vulnerable or exposed individuals. Given the potential for severe impacts of the more intense heat waves that are virtually certain to occur in the warmer future, it is critical that both the physical and social sciences be considered together to enable society to adapt to these conditions.