For years, genomic medicine—medicine based on the growing understanding of the genetic contribution to many diseases and conditions—has been hailed as the future of medical treatment, but it has thus far had limited effect on day-to-day medical practice. The ultimate goal of genomic medicine has always been the ability not just to identify dangerous gene mutations, but to fix them. Now CRISPR and related genome-editing technologies may have the potential to provide a safe and effective way to repair dangerous mutations. In the wake of ethically dubious experiments with human embryos in China, the international governance of human genome editing is emerging as an urgent topic for scientists, regulators, and the public. Efforts to develop a governance model are underway at national and international levels. These efforts are the subject of multiple initiatives by national and international health and science organizations and are topics of discussion at scientific conferences, summits, and meetings. This Article reports on the Authors’ multi-year, interdisciplinary project to identify and investigate the practical, ethical, and policy considerations that are emerging as the greatest concerns about human genome editing, and ultimately to develop policy options. The project involves monitoring the discussions of groups, both government-sponsored and private, that are considering how genome editing should be governed; observing conferences where the topic is discussed; analyzing emerging policy reports by national and international bodies; and interviewing a wide range of stakeholders, including scientists, ethicists, and those who make and comment on public policy. The Article identifies several stakeholder concerns that are especially prominent in the research to date and begins to explore the implications of these concerns for alternative models of governance. There are current indications that, for practical purposes, a focus on “soft,” hybrid forms of governance based on networks of multiple public and private stakeholders may turn out to be the most promising course to pursue. The “new governance” paradigm developed in the corporate and financial sectors offers a useful model for understanding the dynamics of this approach.