Recent decades have seen a series of high-profile public health crises involving viruses, bacteria and other biological agents, together with escalating concern over impacts of biological invasion on crops and ecosystems. In the context of intensifying globalization, such hazards are being viewed as serious ‘security’ threats. For critical social theorists, this growing concern with biosecurity at the global scale has worrying implications, in that it promotes a state of fear over ‘life itself’ which is being used to justify heightened surveillance and increasingly intrusive intervention. However, there are alternative perspectives on living with adventitious and unpredictable biological life. For over a century and a half, ‘settler societies' such as Aotearoa New Zealand and Australia have been grappling with the environmental and economic impacts of non-native organisms running wild. Examining events surrounding an incursion of tussock moths in Auckland, it is argued that biosecurity policy can also be viewed as a flexible and evolving response to uncertainties associated with translocated biological life. Furthermore, the ‘peripheral’ tradition of sustained inquiry around the issue of which organisms belong in which places leads us back to questions about the characteristics of insects themselves and about the dynamics of the environments with which they interact. In this way, critical thinking around biosecurity is opened to a depth of engagement with evolutionary and geological processes that offer new dimensions to thinking about the ‘biopolitics' and ‘geopolitics' of encountering life out of bounds.