Language exerts a powerful influence on our concepts. We review evidence documenting the developmental origins of a precocious link between language and object categories in very young infants. This collection of studies documents a cascading process in which early links between language and cognition provide the foundation for later, more precise ones. We propose that, early in life, language promotes categorization at least in part through its status as a social, communicative signal. But over the first year, infants home in on the referential power of language and, by their second year, begin teasing apart distinct kinds of names (e.g. nouns, adjectives) and their relation to distinct kinds of concepts (e.g. object categories, properties). To complement this proposal, we also relate this evidence to several alternative accounts of language's effect on categorization, appealing to similarity ('labels-as-features'), familiarity ('auditory overshadowing'), and communicative biases ('natural pedagogy').