The past decades in the UK have witnessed renewed interest by policymakers, research funders and research institutions in the engagement of non-academic individuals, groups and organizations with research processes and products. There has been a broad consensus that better engagement leads to better impact, as well as significant learning around understanding engagement and improving practice. However, this sits in tension to a parallel trend in British higher education policy that reduces the field to a narrow definition of quantitatively measured impacts attributed to individual researchers, projects and institutions. In response, this article argues for the mobilization of an emerging field of 'research engagement studies' that brings together an extensive and diverse existing literature around understandings and experiences of engagement, and has the potential to contribute both strategically and conceptually to the broader impact debate. However, to inform this, some stocktaking is needed to trace the different traditions back to their conceptual roots and chart out a common set of themes, approaches and framings across the literature. In response, this article maps the literature by developing a genealogy of understandings of research engagement within five UK-based domains of policy and practice: higher education; science and technology; public policy (health, social care and education); international development; and community development. After identifying patterns and trends within and across these clusters, the article concludes by proposing a framework for comparing understandings of engagement, and uses this framework to highlight trends, gaps and ways forward for the emerging field.