ABSTRACT. One of the practices that has defined the ethos of genomic research to date is a commitment to open and rapid sharing of genomic data and resources. As genomic research evolves into an international enterprise, this commitment is being challenged by the need to respect the interests of those it involves and implicates, from individual scientists and subjects to institutions and nations. In this essay, we first describe the types of claims that different stakeholders are making about the disposition of genomic data and samples. Next, we illustrate the complexities of these multiple claims by applying them to the case of one ongoing international genomics initiative, the H3Africa Consortium. Finally, in the light of these complexities, we conclude by comparing and contrasting four governance models for future international data-sharing policy and practices in genomics.