Immigrants in OECD countries have become increasingly highly skilled and more positively selected between 1980 and 2010. This paper analyses the factors driving these trends focusing on Switzerland, which experienced large immigration inflows and similar trends. Our findings suggest that skill-biased demand shifts in destinations and education upgrading in the origin countries of immigrants are the most important determinants. Yet, while education upgrading predicts only a modest increase in tertiary and a larger increase in secondary education, we show that skill-biased demand shifts are crucial to understand why tertiary education increased sharply among newly-arriving immigrants while the share of secondary educated among them merely stabilized. Additionally, we show that our results are not driven by immigration policies