The concept of equality of opportunity (EOp) goes back to Roemer (1993, 1998) who argues that a society shall guarantee its members equal access to advantage regardless of their circumstances, while holding them responsible for turning that access into actual advantage by the application of effort. Such arguments have been on the political agenda across the European Union, where the recent enlargements have brought together countries with rather different economic, social, and political backgrounds. This paper investigates how family background influences income acquisition in 15 European countries. It also scrutinizes how governments affect EOp through the design of their tax and transfer schemes. Our overall results suggest that the link between family background and economic success is usually tighter in relatively poor countries than in rich countries. Moreover, we find a clear country clustering for the Scandinavian, the Continental European, and the Anglo-Saxon countries. For Eastern Europe, our results are less definite. Looking at the impact of the tax and benefit schemes in the EU, it can be concluded that both taxes and transfers reduce inequality of opportunities, with social benefits typically playing the key role. Furthermore, the equalizing impacts of the tax benefit system on inequality of opportunity differ substantially from the ones observed when referring to the traditional notion of inequality of outcomes.