Research to date suggests that infants exploit statistical regularities in linguistic input to identify and learn a range of linguistic structures, ranging from the sounds of language (e.g., native-language speech sounds, word boundaries in continuous speech) to aspects of grammatical structure (e.g., lexical categories like nouns and verbs, basic aspects of syntax). This article presents a brief review of the infant statistical language learning literature, and raises broader questions concerning why infants are sensitive to statistical regularities. In doing so, we consider the relationship between statistical learning, prediction, and uncertainty reduction in infancy.