Definitions of heritage languages include the languages of migrant, indigenous, and national minorities. This chapter is concerned with migrant minorities. The EU is generally pictured as valuing multilingualism, as reflected by EU policies and citizen’s attitudes. Nevertheless, when Europeans think and speak about protecting multilingualism, they do not necessarily have migrant languages in mind, although these are more numerous than other minorities in terms of both language diversity and number of speakers. The chapter summarizes linguistic research on HSs in Europe covering early childhood, primary school/adolescence, and adulthood, making reference to (morpho-)syntax, phonology, and vocabulary. The goal is to uncover common outcomes and missing links. The focus differs across these research areas but crosslinguistic influence is a common denominator, and the examples witness that research has gone beyond highlighting differences between monolinguals and HSs. Scenarios suggest that HSs may anticipate or resist language change, and that adult HSs often stay within the limits of what is possible in the baseline or related varieties. I conclude by pointing out the lack of comparisons across generations, an overrepresentation of specific languages families, and by suggesting that research drawing analogies with other situations of language contact and change are highly desirable.