Wet bulb globe temperature (WBGT), a combined measure of temperature and humidity effects on thermal comfort, is used to define heat stress waves (HSWs). While emerging research has raised concerns on future changes in heat stress, for the first time, this study examines spatiotemporal changes in multiple HSW characteristics (intensity, duration, frequency, and cumulative mean intensity) in the 21st century under three emissions scenarios. It is the sustained nature of HSWs that impose more adverse impacts than extreme heat on a single day. HSWs are expected to be more intense, persistent, frequent, and influential due to anthropogenic influence. Models project the largest increases in multiple HSW characteristics will occur over the tropics and subtropics. The exception is maximum intensity, which displays a relative uniform increase over most global land areas. Analysis of regional population exposure to HSWs under different climate and socioeconomic scenarios emphasizes the importance of aggressive mitigation to minimize the potential impacts of HSWs. We further investigate how different regional HSW characteristics are projected to change relative to increasing global mean surface temperature (GMST). Our results confirm the varying rates and different trajectories at which regional HSWs change, independent of forcing pathway, strongly related to GMST. On both globally aggregated and regional scales, the maximum intensity and GMST are highly linearly associated, with an approximately 1:1 increase. However, the other three HSW characteristics are projected to change at a nonlinear rate per degree of GMST increase in general and display large regional variation in the rates of their changes. Plain Language Summary Besides air temperature, air humidity is another important factor in determining the impact of heat waves on humans. High humidity will reduce the efficiency of evaporative cooling and, when combined with high temperature, could pose a serious threat to human health or even life safety. Heat stress indices, taking into account both temperature and humidity effects, are considered to be better indicators of environmental conditions conducive to heat stress on human health. We here employ a widely used heat stress index, wet bulb globe temperature, to define heat waves, namely, heat stress waves (HSWs). Heat waves can be considered through a number of characteristics, and it is their distinctive characteristics that result in the vast array of adverse impacts. This also applies to HSWs. Our results show that more intense, longer-lasting, frequent, and influential HSWs are anticipated during the 21st century, and anthropogenic warming substantially increases the occurrence of HSWs. Except intensity, tropical regions will generally witness the largest increases in multiple HSW characteristics and the number of people that may be exposed to HSWs. Changes in HSW characteristics are confirmed not to depend on whether a particular warming is reached sooner or later; they are strongly related to global mean sur...