How do children learn to communicate, and what do they learn? Traditionally, most theories have taken an associative, compositional approach to these questions, supposing children acquire an inventory of form-meaning associations, and procedures for composing / decomposing them; into / from messages in production and comprehension. This paper presents an alternative account of human communication and its acquisition based on the systematic, discriminative approach embodied in psychological and computational models of learning, and formally described by communication theory. It describes how discriminative learning theory offers an alternative perspective on the way that systems of semantic cues are conditioned onto communicative codes, while information theory provides a very different view of the nature of the codes themselves. It shows how the distributional properties of languages satisfy the communicative requirements described in information theory, enabling language learners to align their expectations despite the vastly different levels of experience among language users, and to master communication systems far more abstract than linguistic intuitions traditionally assume. Topics reviewed include morphological development, the acquisition of verb argument structures, and the functions of linguistic systems that have proven to be stumbling blocks for compositional theories: grammatical gender and personal names.