Statistical learning—sensitivity to distributional patterns in the input—has emerged as a key mechanism for language learning. In this talk, I will argue that statistical learning alone is not sufficient to account for the full complexity of human language use—only when combined with feedback can successful learning be accomplished. To support this argument, I report on three lines of research. A psycholinguistic study details the role of positive, negative, and mixed feedback on the gradual learning of language-like statistical regularities within an active guessing game paradigm. Additional findings from an iterated learning study demonstrate that feedback is needed for languages to maintain multiple alternative word orders (like in Turkish) across ‘generations’ of human learners. Finally, results from experiments with different versions of GPT-3 underscore the importance of feedback for Large Language Models to reach human-like performance. Together, the three studies suggest that complex language use requires the incorporation of interactive feedback into the learning process.