Using PISA and PIAAC data from twelve OECD countries, we examine the gap in cognitive skills among immigrants and natives and evaluate how those differences have evolved over time. We also consider how demographics, family background and school quality explain the development of cognitive skills of young people with immigrant backgrounds. The results show, first, that some convergence in skills occurs between secondgeneration immigrants and natives over time. Second, demographics, family background and school quality variables all contribute to the achievement gaps across different groups.