The future paths of population ageing result from specific combinations of declining fertility and increasing life expectancies in different parts of the world. Here we measure the speed of population ageing by using conventional measures and new ones that take changes in longevity into account for the world as a whole and for 13 major regions. We report on future levels of indicators of ageing and the speed at which they change. We show how these depend on whether changes in life expectancy are taken into account. We also show that the speed of ageing is likely to increase over the coming decades and to decelerate in most regions by mid-century. All our measures indicate a continuous ageing of the world's population throughout the century. The median age of the world's population increases from 26.6 years in 2000 to 37.3 years in 2050 and then to 45.6 years in 2100, when it is not adjusted for longevity increase. When increases in life expectancy are taken into account, the adjusted median age rises from 26.6 in 2000 to 31.1 in 2050 and only to 32.9 in 2100, slightly less than what it was in the China region in 2005. There are large differences in the regional patterns of ageing. In North America, the median age adjusted for life expectancy change falls throughout almost the entire century, whereas the conventional median age increases significantly. Our assessment of trends in ageing is based on new probabilistic population forecasts. The probability that growth in the world's population will end during this century is 88%, somewhat higher than previously assessed. After mid-century, lower rates of population growth are likely to coincide with slower rates of ageing.