Public policy must confront emergencies that evolve in real time and in uncertain directions, yet little is known about the nature of policy response. Here we take the coronavirus pandemic as a global and extraordinarily consequential case, and study the global policy response by analyzing a novel dataset recording policy documents published by government agencies, think tanks, and intergovernmental organizations (IGOs) across 114 countries (37,725 policy documents from Jan 2nd through May 26th 2020). Our analyses reveal four primary findings. (1) Global policy attention to COVID-19 follows a remarkably similar trajectory as the total confirmed cases of COVID-19, yet with evolving policy focus from public health to broader social issues. (2) The COVID-19 policy frontier disproportionately draws on the latest, peer-reviewed, and high-impact scientific insights. Moreover, policy documents that cite science appear especially impactful within the policy domain. (3) The global policy frontier is primarily interconnected through IGOs, such as the WHO, which produce policy documents that are central to the COVID19 policy network and draw especially strongly on scientific literature. Removing IGOs' contributions fundamentally alters the global policy landscape, with the policy citation network among government agencies increasingly fragmented into many isolated clusters. (4) Countries exhibit highly heterogeneous policy attention to COVID-19. Most strikingly, a country's early policy attention to COVID-19 shows a surprising degree of predictability for the country's subsequent deaths. Overall, these results uncover fundamental patterns of policy interactions and, given the consequential nature of emergent threats and the paucity of quantitative approaches to understand them, open up novel dimensions for assessing and effectively coordinating global and local responses to COVID-19 and beyond.