Biobanks are an integral part of contemporary biomedical and biotechnological research, nationally and internationally. Over time, biobanking has also become invariably more transnationalised, following broader developments of biomedical research across borders and the increasing transnational circulation of human specimen and related data. The manifold technical, legal, ethical and governance challenges resulting from such transboundary, potentially global, circulation of human specimens and related data, however, have to date not resulted in any binding truly international agreement regulating transnational issues with biobanking. In this paper, we analyse when and in what way biobanking has been subject to policy debates in international organisations, with a particular interest in the most prominent policy frames that have informed these debates. We identify biobanking as an underexplored area of research on international policy-making, notwithstanding its prominence in global health cooperation and the many contentious issues that surround it. Our empirical analysis traces the diversification of policy frames over time (1995 to 2019) and, zooming in on those policy frames that emerge as salient yet contested in our analysis, exposes the trajectories of debates on the rules and norms that should govern the transnational circulation and commodification of the human body. We find that biobanking has evolved from a technical, apolitical matter into a multi-faceted issue, which is reflected in the diversification of frames circulating in international organisations. On the basis of our study, we identify a number of policy frames that have emerged as particularly contested over time, with human rights frames standing out as having the most divisive potential.