With dramatic declines in fertility taking place throughout the world, it is increasingly important to understand the demographic transition as a global process. While this universality was a cornerstone of classic transition theories, for many decades it was largely neglected by experts because fertility in the developing world did not seem to follow the expected pattern. When comparing earlier and more recent transition experiences, important similarities and disparities can be seen. Everywhere mortality decline appears to have played a central role for fertility decline. The differences in the timing of the response of fertility to mortality decline, with very small gaps historically and prolonged ones in more recent transitions, plus the much more rapid decline in vital rates in many developing countries, constitute an important challenge to any general explanation of the process. The specific characteristics of recent transitions have led to decades of higher population growth rates, and promise to give way to much more rapid dynamics of population ageing in many countries. This may limit the ability of newcomers to take full advantage of the demographic transition for the social and economic modernisation of their societies. Copyright © 2004 John Wiley & Sons, Ltd.