Large increases in joint heat-humidity extremes are a robust feature of climate projections, more so than increases in either variable independently. The wet-bulb temperature threshold of 35°C is considered particularly important, corresponding to the level at which it is impossible for the human body to maintain homeostasis. Our analysis of more than 7500 global weather stations from HadISD reveals that instances of 35°C have already been briefly but reliably recorded in some cities of the coastal Middle East. Additionally, South Asia and coastal areas throughout the subtropics regularly experience values perilously close to this threshold. Station and ERA-Interim reanalysis data both indicate that the most extreme heat-humidity combinations have increased significantly over the 1979-2017 period. We develop and employ a generalized-extreme-value model to estimate that the 30-year return value of global-maximum wet-bulb temperature at ERA-Interim resolution will exceed 35°C when global-mean temperature has risen between 1.5°C and 2.0°C above the pre-industrial, masking even higher values at smaller spatial scales. The occurrence in the coming decades of such severe heat and humidity over large populated regions represents a situation never before experienced. We also present observational evidence that these wet-bulb temperature extremes are fostered by locally high SSTs as well as modulated by regional dynamics such as monsoons. Large-scale climate modes of variability, such as ENSO, lead to highly correlated interannual variability between the number of global exceedances of different wet-bulb temperature thresholds. Overall, our results show that the wet-bulb temperature ‘safety margin’ between currently reported values and 35°C is both smaller than previously understood and rapidly shrinking, presenting a serious challenge to human survival in the hottest and most humid places on Earth.