Emphasizing the context of what has often been referred to as "scarce natural resources", in particular forests, meadows, and fishing stocks, Elinor Ostrom's important works, including Governing the commons (1990) and Understanding institutional diversity (2005), present an institutional framework for discussing the development and use of collective action with respect to environmental problems. In this article we discuss extensions of Ostrom's approach to human genes and genomes and explore its limits and usefulness in this field. We argue that while there are radically different contexts and cases and governance regimes still to be debated, what we call "genomic stuff" -genomic material, data, and information -often can best be regulated by modes of stewardship and self-regulation of appropriators. We exemplify this claim by a discussion of gene patenting, the "Genome War", and the so-called HapMap project. The issue of how to best govern the genomic stuff of humans, we suggest, is complicated by the situation that the appropriator and the appropriated can be the same, inviting fundamental questions about politics and ethics.