Developments in genomic science and its applications raise significant public policy issues. Restrictive governance regimes can inhibit progress that has the potential to significantly enhance social and economic outcomes. But permissive regimes run the risk of mistakes, inappropriate management practices, and accidents having costly effects on human populations, various agricultural activities, and ecosystems. This article provides an overview of genomic science. We survey public policy issues raised by this science and how existing public policy models and approaches have been used to consider and address them. Issues covered include the quality of the science, non-human applications, human applications, and social impacts. From here, attention turns to challenges posed both at the conceptual and practical level that are expected to promote further policy learning. We consider the need for effective oversight and regulatory regimes, and greater transparency and participation in decision-making. The article also introduces the other contributions to this theme issue of Policy and Society.