In recent years, growing economic globalisation has been accompanied by rising social support for market systems as a means of managing resource-use. In turn, the free market movement considers definite and secure property rights (especially private rights and, sometimes, communal rights) in resources to be the necessary basis for a desirable market system. Global policies for managing the Earth’s genetic resources have been influenced by this approach. As outlined in this article, there has been a global expansion of property rights in genetic resources, and further extensions have been advocated. In order to assess the possible social benefits and costs of granting property rights in genetic resources, they are classified. This classification is shown to be useful in discussing economic and legal reasons for granting or denying property rights in genetic resources. Furthermore, it is shown to be pertinent to the consideration of market failures that may accompany the granting of property rights in genetic resources and which limit the potential social economic benefits from establishing property rights in these resources. It is concluded that many advocates of managing genetic resources by means of secure property rights and market systems have been overly optimistic about the potential of this policy, its social benefits, its impact on the conservation of biodiversity, and its workability. There is a need for more informed debate on these matters before concluding that wholesale global extension of property rights in genetic material is desirable.