As the climate becomes warmer on average, it makes intuitive sense that we will see more hot days and we've had predictions of this for some time. However, the duration of heatwaves — how many days in a row exceed a temperature that is unusually hot for a given region — can be very important for impacts on humans, livestock and ecosystems. Predicting how these durations will change under a long-term warming trend is more challenging because day-to-day temperatures are correlated — tomorrow's temperatures have a dependence on today's temperature. This study takes this effect into account, along with the warming seen in current and historical observations and projected for the future by climate models for a wide range of land regions. Not only do the heatwave durations increase, but each additional increment of warming causes a larger increase in the typical length of long heat waves. In other words, if the next decade brings as much large-scale warming as a previous decade, the additional increase in heatwave durations would be even larger than we've experienced so far.