The robustness and flexibility of human language is underpinned by a machinery of interactive repair. Repair is deeply intertwined with two core properties of human language: reflexivity (it can communicate about itself) and accountability (it is used to publicly enforce social norms). We review empirical and theoretical advances from across the cognitive sciences that mark interactive repair as a domain of pragmatic universals, a key place to study metacognition in interaction, and a system that enables collective computation. This provides novel insights into the role of repair in comparative cognition, language development, and human-computer interaction. As an always-available fallback option and an infrastructure for negotiating social commitments, interactive repair is foundational to the resilience, complexity, and flexibility of human language.