Introducing a special issue of Policy Design and Practice on designing future governments, this article draws on growing interest in the concepts and practices of anticipation, foresight and design among policy makers in international bodies, think tanks and governments. Building on the concept of anticipatory governance, we aim to show how approaches associated with foresight and design produce a capacity for future uncertainties to be made visible and graspable, with the potential to open up participation and reflexivity in discussions about public policy issues and anticipate ways to address them, beyond public administrations. The special issue includes six papers sharing insights about scenarios, workshops, public innovation labs and co-design projects from Europe, Latin America and Australia. Some are speculative—based on a small-scale intervention or experiment—while others are based on a larger scale project with the participation of relevant stakeholders such as public service providers, public administrations and local residents. Together, the contributions to the special issue suggest that futures and design approaches enact an anticipatory logic which is necessary for public administrations to achieve their goals, in the face of many uncertainties and in a context in which new forms of expertise, data and infrastructures are opening up government.