How do children acquire a language? Decades of work have provided a roadmap of principles and mechanisms for early language learning as attested by small-scale laboratory tasks. But there is not yet a convincing empirical synthesis of this work that addresses both the systematicity and ubiquity of language learning and the variability of learning trajectories across children. In this talk I will describe some initial steps towards such a synthesis. This research integrates high-density data from individual children learning a single language and summary data from tens of thousands of children learning more than a dozen languages. Taken together, the data support a hybrid picture in which children slowly accumulate knowledge in rich social contexts but also show evidence for surprisingly fast grammatical abstractions.