Having an adequate and extensively recognized resource governance system is essential for the conservation and sustainable use of crop genetic resources in a highly populated planet. Despite the widely accepted importance of agrobiodiversity for future plant breeding and thus food security, there is still pervasive disagreement at the individual level on who should own genetic resources. The aim of the article is to provide conceptual clarification on the following concepts and their relation to agrobiodiversity stewardship: open access, commons, private property, state property and common heritage of humankind. After presenting each property regime, we will examine whether and how these incentivize the conservation, improvement and sharing of crop genetic resources, and conclude by defending a mixed property regime.