The study of language acquisition has a long and contentious history: researchers disagree on what drives this process, the relevant data, and the interesting questions. Here, I outline the Starting Big approach to language learning, which emphasizes the role of multiword units in language, and of coarse-to-fine processes in learning. I outline core predictions and supporting evidence. In short, the approach argues that multiword units are integral building blocks in language; that such units can facilitate mastery of semantically opaque relations between words; and that adults rely on them less than children, which can explain (some of) their difficulty in learning a second language. The Starting Big approach is a theory of how children learn language, how language is represented, and how to explain differences between first and second language learning. I discuss the learning and processing models at the heart of the approach and their cross-linguistic implications.