Our research on statistical language learning shows that infants, young children, and adults can compute, online and with remarkable speed, how consistently sounds co-occur, how frequently words occur in similar contexts, and the like, and can utilize these statistics to find candidate words in a speech stream, discover grammatical categories, and acquire simple syntactic structure in miniature languages. However, statistical learning is not merely learning the patterns presented in the input. When their input is inconsistent, children sharpen these statistics and produce a more systematic language than the one to which they are exposed. When input languages inconsistently violate tendencies that are widespread in human languages, learners shift these languages to be more aligned with language universals, and children do so much more than adults. These processes explain why children acquire language (and other patterns) more effectively than adults, and also may explain how systematic language structures emerge in communities where usages are varied and inconsistent. Most especially, they suggest that usage-based learning approaches must account for differences between adults and children in how usage properties are acquired, and must also account for substantial changes made by adult and child learners in how input usage properties are represented during learning.