Background: Recent complex and cross-boundary policy problems, such as climate change, pandemics, and financial crises, have recentred debates about state capacity, democratic discontent and the 'crisis of expertise'. These problems are contested and open to redefinition, misunderstanding, spin, and deception, challenging the ability of policymakers to locate, discriminate, comprehend, and respond to competing sources of knowledge and expertise. We argue that 'non-knowledge' is an under-explored aspect of responses to major policy crises. Key points: While discussed in recent work in sociology and other social sciences, non-knowledge has been given less explicit attention in policy studies, and is not fully captured by orthodox understandings of knowledge and evidence use. We outline three main forms of non-knowledge that challenge public agencies: amnesia, ignorance and misinformation. In each case, 'non-knowledge' is not simply the absence of policy-relevant knowledge. Amnesia refers to what is forgotten, reinvented or 'unlearned', while claims of ignorance involve obscuring or casting aside of relevant knowledge that could (or even should) be available. To be misinformed is to actively believe false or misleading information. In each instance, non-knowledge may have strategic value for policy actors or aid the pursuit of self-interest. Conclusions and implications: We demonstrate the relevance of non-knowledge through a brief case study, emerging from the inquiry into the COVID-19 hotel quarantine programme in the Australian state of Victoria. We argue that both amnesia and 'practical' forms of ignorance contributed to failures during the early part of the programme.