We introduce our comparative study on minority and majority youth in four European countries by presenting the problem, basic concepts, theoretical starting points and our strategy of analysis. We address differences in integration across (i) immigrant generations (exposure), (ii) immigrant origin groups and (iii) receiving countries, for several indicators of structural, cultural and social integration. We find few and unsystematic differences in integration across receiving countries. Integration is quite remote for some aspects of social and cultural integration and slowest for those originating in poorer regions at greater cultural and socioeconomic distances, such as the Middle East and Africa. Exposure to the host country leads to decreasing differences in language proficiency and host country identification, but not in liberal attitudes and tolerance, religion and religiosity, or inter-ethnic friendships. We conclude that lingering differences should partly be understood against a backdrop of deeply entrenched structural phenomena such as socialisation, stratification and segregation.