Synthetically-constructed gene drives, that use CRISPR-Cas9 technology to bias inheritance of a particular gene, have been proposed for exotic pest eradication. This is a controversial idea, as there is an apparent potential risk in the use of such technologies, for example to non-target populations of the species. Further, the basic question — Is the technology actually able to achieve its goal in practice? — is vexed. I will discuss some of our work which has developed stochastic, individual-based models of a number of gene drive strategies that have been proposed for the possible eradication of exotic vertebrate pests. I will discuss some of the issues surrounding their likely effectiveness for eradication, explore the potential risks to non-target populations, along with considering options for alleviating these issues.