This special issue reports on a cross-linguistic study of other-initiated repair, a domain at the crossroads of language, mind, and social life. Other-initiated repair is part of a system of practices that people use to deal with problems of speaking, hearing and understanding. The contributions in this special issue describe the linguistic resources and interactional practices associated with other-initiated repair in ten different languages. Here we provide an overview of the research methods and the conceptual framework. The empirical base for the project consists of corpora of naturally occurring conversations, collected in fieldsites around the world. Methodologically, we combine qualitative analysis with a comparative-typological perspective, and we formulate principles for the cross-linguistic comparison of conversational structures. A key move, of broad relevance to pragmatic typology, is the recognition that formats for repair initiation form paradigm-like systems that are ultimately language-specific, and that comparison is best done at the level of the constitutive properties of these formats. These properties can be functional (concerning aspects of linguistic formatting) as well as sequential (concerning aspects of the interactional environment). We show how functional and sequential aspects of conversational structure can capture patterns of commonality and diversity in conversational structures within and across languages