In seeking to counter adverse economic impacts resulting from the COVID-19 pandemic, many governments quickly announced major infrastructure stimulus packages alongside a series of governance reforms to speed delivery. Despite significant differences between political, institutional and policy contexts of countries, clear trends emerged, most notably discourses of promise promoting the possibilities of state-led infrastructure allied to reforms to expedite delivery. Using case studies of Australia, Aotearoa-New Zealand and the UK, we draw upon theories of postpolitics and states of exception to explain how these approaches comprise a form of infrastructuralism that both elevates the criticality of infrastructure at the same time as depoliticising infrastructure planning. We argue that the promises of Building Back Better did not constitute the radical rupture from earlier practices initially promised and that in future crises we need to resist the closure of political space that typically accompanies emergency measures and ask ‘what infrastructure, for whom and where?’