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Science is increasingly a collaborative pursuit. Although the modern scientific enterprise owes much to individuals working at the core of their field, humanity is increasingly confronted by highly complex problems that require the integration of a variety of disciplinary and methodological expertise. In 2016, the U.S. National Science Foundation launched an initiative prioritizing support for convergence research as a means of “solving vexing research problems, in particular, complex problems focusing on societal needs.” We discuss our understanding of the objectives of convergence research and describe in detail the conditions and processes likely to generate successful convergence research. We use our recent experience as participants in a convergence workshop series focused on resilience in the Arctic to highlight key points. The emergence of resilience science over the past 50 years is presented as a successful contemporary example of the emergence of convergence. We close by describing some of the challenges to the development of convergence research, such as timescales and discounting the future, appropriate metrics of success, allocation issues, and funding agency requirements.