Studies of preverbal infants exposed to a bilingual environment have unveiled the existence of important similarities, but also significant differences in the way monolinguals-to-be and bilinguals-to- be solve the problem of language acquisition. In this talk I will review the evidence that shows how very young babies can differentiate the languages of their environment, how they learn the sounds of their languages, and how they learn the very first words.  These studies provide important clues to the nature of the successful solutions bilingual babies develop to learn two languages and to become competent adult bilingual speakers.