Recent years have seen a dramatic growth in interest in the nature and extent of co-production in the health and social care sectors. Due to the proliferation of work on co-production, there is variation in practice in how co-production is defined, understood, and used in practice. We conducted a narrative review to explore, and provide an overview of, which models of health and social care co-production have been developed, applied, and critiqued over recent decades. Seventy-three peer-reviewed articles met our inclusion criteria. In this set of articles, we identified three broad types of models: conceptual/theoretical, practice-oriented, and presenting a typology. We found that practice-oriented models, predominantly from the Health Services Research and Quality Improvement literature, had largely not drawn on conceptual/theoretical models from the disciplinary fields of Public Administration & Management and Sociology. In particular, they have largely neglected theoretical perspectives on relationships and power and agency in co-production work. The concepts of Service-Dominant Logic and Public Service-Dominant Logic as ways to think about the joint, collaborative process of producing new value, particularly in the context of the use of a service, have also been neglected. Our review has identified distinct literatures which have contributed a variety of models of health and social care co-production. Our findings highlight under-explored dimensions of co-production that merit greater attention in the health and social care contexts. The overview of models of co-production we provide aims to offer a useful platform for the integration of different perspectives on co-production in future research and practice in health and social care.