Demographic trends underlie a great many economic and social processes. However, because populations tend to change relatively slowly, demography is often taken for granted and its impact under-appreciated. Rather like some slow geological process that is imperceptible in the short run, demographic change often has an ineluctable force, and ends up changing the whole social and economic landscape. When trying to understand the relationship between the European Union and its neighbours to the South and East of the Mediterranean, an understanding of the demographic forces at work is essential. In this chapter I will present an outline of the main demographic trends in Europe and the Mediterranean over the last half century, and will look forward to sketch the most likely developments for the coming decades. The EU and its neighbours do not only share the Mediterranean, we also share a common future and demographic trends will play a crucial role in determining the nature of that future.