It is now certain that human-induced climate change is increasing the incidence of extreme temperature, precipitation and drought events globally. A critical aspect of these extremes is their potential concurrency that can result in substantial impacts on society and environmental systems. Therefore, quantifying concurrent extremes in current and projected climate is necessary to take measures and adapt to future challenges associated with such conditions. Here we investigate changes in individual and concurrent extremes in multi-model simulations of the sixth phase of the Coupled Model Intercomparison Project (CMIP6) for different global warming levels (GWLs). We focus on the individual and simultaneous occurrence of the extreme events, encompassing heatwaves, droughts, maximum 1 d precipitation (Rx1day), and extreme wind (wind), as well as the compound events heatwave–drought and Rx1day–wind in the pre-industrial period (1850–1900; reference period), for approximately present conditions (+1 ∘C of global warming), and at three higher global warming levels (GWLs of +1.5, +2 and +3 ∘C). We focus our analysis on 139 countries and three climatic macro-regions: northern mid- and high-latitude countries (MHC), subtropical countries (STC), and tropical countries (TRC). We find that, on a global scale, most individual extremes become more frequent and affect more land area for higher GWLs. Changes in frequency of individual heatwaves, droughts, Rx1day and extreme wind with higher GWLs cause shifts in timing and disproportionate increases in frequency of concurrent events across different months and different regions. As a result, concurrent occurrences of the investigated extremes become 2.0 to 9.6 times more frequent at +3 ∘C of global warming compared to the pre-industrial period. At +3 ∘C the most dramatic increase is identified for concurrent heatwave–drought events, with a 9.6-times increase for MHC, an 8.4-times increase for STC and a 6.8-times increase for TRC compared to the pre-industrial period. By contrast, Rx1day–wind events increased the most in TRC (5.3 times), followed by STC (2.3 times) and MHC (2.0 times) at +3 ∘C with respect to the pre-industrial period. Based on the 2015 population, these frequency changes imply an increase in the number of concurrent heatwave–drought (Rx1day–wind) events per capita for 82 % (41 %) of countries. Our results also suggest that there are almost no time periods (on average 0 or only 1 month per year) without heatwaves, droughts, Rx1day and extreme wind for 21 countries at +1.5 ∘C of global warming, 37 countries at +2 ∘C and 85 countries at +3 ∘C, compared to 2 countries at +1 ∘C of global warming. This shows that a large number of countries will shift to near-permanent extreme conditions even at global warming levels consistent with the limits of the Paris Agreement. Given the projected disproportionate frequency increases and decreasing non-event months across GWLs, our results strongly emphasize the risks of uncurbed greenhouse gas emissions.