Linguistics research has traditionally been shaped by the idea of a native monolingual speaker. Research on bilingualism and language learning has also defined stages and features of bilinguals in terms of differences (‘advantages’ or ‘disadvantages’) with respect to native monolingual norms. However, real monolingualism is becoming rarer in our communities because more people learn other languages or are simply exposed to multilingualism in society. In addition, research has shown that a speaker’s first language changes in selective and predictable ways upon exposure to a second language, which provides strong arguments against the implicitly held view that bilinguals are (or should behave like) two monolinguals in one. Understanding the new emerging picture requires an interdisciplinary effort that combines the strengths of linguistic, cognitive and social models and redefines the way we do research on bilingualism and, more generally, on language.