A perspective from semantics is one that pays attention to the meaning of words, and this includes the words in the title of this chapter. What do we mean, then, by bilingualism and what do we mean by cognition? In this article I will focus predominantly on the second of these questions, but I do want to make one point in relation to the first: there is a difference between ‘bilingualism’ in the sense of ‘being able to speak’ two languages and ‘bilingualism’ in the sense of ‘living with’ two languages. As I will discuss more fully in the conclusion, it is bilingualism in this second sense which is now increasingly recognized as a vital source of insight into human cognition in general.