This paper documents assimilation of immigrants in European destinations along cultural, civic, and economic dimensions, distinguishing by immigrants' generation, duration of stay, and origin. Based on the European Social Survey, it suggests that assimilation may have multiple facets, and take place at different speed depending on the outcome in question. While assimilation along some economic and cultural outcomes may be correlated, such correlations are not systematic, and imply that progress on some dimensions may compensate the lack of progress on other dimensions; and also that a big discrepancy in one dimension is not necessarily a handicap, or an impediment, for assimilation on other grounds. Correlation of immigrants' outcomes and specific policies aimed at immigrants' integration are rather disparate, raising further questions regarding both their effectiveness and differentiated effect on various aspects of life.