Infrastructures have proven to be useful focal points for understanding social phenomena. The projects of concern in this literature are often considered complete or, if not, their materialization is assumed to be imminent. However, many—if not most—of the engineered artifacts and systems classified as infrastructure exist in states aptly characterized as unbuilt or unfinished. Bringing together scholarship on unbuilt and unfinished infrastructures from anthropology, architecture, geography, history, and science and technology studies, this article examines the ways in which temporalities articulate as planners, builders, politicians, potential users, and opponents negotiate with a project and each another. We develop a typology of heuristics for analyzing the temporalities of the unbuilt and unfinished: shadow histories, present absences, suspended presents, nostalgic futures, and zombies. Each heuristic makes different temporal configurations visible, suggesting novel research questions and methodological approaches.