Extreme heat events cause significant societal impacts, prompting much concern and research about possible changes to their frequency and intensity as the climate warms. However, to date, extremes in air temperature have been emphasised at the expense of ‘heat-humidity’ indices, measures which incorporate the effect of atmospheric latent heat content on heat stress and provide a more complete picture of the thermal environment for human thermoregulation. This progress report restores balance by reviewing recent developments in the understanding of how heat-humidity indices have changed, and may continue to, as the climate warms further. The literature indicates that a concurrent rise in temperature and absolute humidity has already increased the frequency of potentially deadly conditions, and has reduced labour potential worldwide. More serious consequences may result if mitigation efforts are unsuccessful. The energetic basis of a heat-humidity perspective has permitted researchers to identify, for example, that by the end of the century, substantial parts of the Earth’s surface may be too hot and humid for human thermoregulation. Such consequences are avoided for less pessimistic scenarios of climate warming, but the societal impacts may still be very severe, as densely-populated low-latitude environments emerge as particularly at risk when a humid heat perspective is adopted. Counter to air temperature, changes in mean heat-humidity indices are actually amongst the largest worldwide at lower latitudes, where only small increases in the mean may be required to substantially enhance the frequency of dangerous conditions. The report concludes by outlining areas requiring improved process understanding, and it highlights the urgent role for societal adaptation if the worst impacts from rising humid heat are to be avoided.