Migrants into European countries are often less educated than European natives. We analyse whether migrants' children are more or less likely than natives' children to achieve upward educational mobility across generations, and study differences in the factors, which contribute to differences in mobility for the two groups. We find that migrants' descendants are more often upwardly mobile (and less often downwardly mobile) than their native peers in the majority of countries studied, and show that the main factor contributing to these patterns is the education level of parents. Although a lower parental education means that their children are less likely to access the same amount of human, social and financial capital as children of more highly educated parents, migrants' descendants over the last two generations were able to make significant progress in reducing education gaps with natives.