We analyse the effects of demographic and education changes on unemployment rates in Europe. Using a panel of European countries for the 1980-2000 period - disaggregated by cohort, gender and education -, we empirically test the economic effects of two stylised facts that have occurred in recent decades: the "baby bust" and the "education boom". We find that structural shifts in the population age structure play an important role and that a lot of variation is also attributable to educational changes, the latter usually neglected in aggregate studies. Results show that demographic and education shocks are qualitatively different for young (adult) workers as well as for more (less) educated people. While adult workers and more educated individuals, in general, experience lower unemployment rates, changes in the population age structure appear to be positively related to young workers' unemployment rates while they have no effect on adults. Conversely changes in the skill structure ("education boom"), even when controlling for skill-biased technological change, reduce the unemployment of the more educated. Labour market institutions also influence unemployment rates in different ways. Unemployment benefits are found to have a positive impact on unemployment, while bargaining coordination and employment protection reduce it.