In recent years, a dramatic increase in the study of infrastructure has occurred in the social sciences and humanities, following upon foundational work in the physical sciences, architecture, planning, information science, and engineering. This article, authored by a multidisciplinary group of scholars, probes the generative potential of infrastructure at this historical juncture. Accounting for the conceptual and material capacities of infrastructure, the article argues for the importance of paradox in understanding infrastructure. Thematically the article is organized around three key points that speak to the study of infrastructure: ruin, retrofit, and risk. The first paradox of infrastructure, ruin, suggests that even as infrastructure is generative, it degenerates. A second paradox is found in retrofit, an apparent ontological oxymoron that attempts to bridge temporality from the present to the future and yet ultimately reveals that infrastructural solidity, in material and symbolic terms, is more apparent than actual. Finally, a third paradox of infrastructure, risk, demonstrates that while a key purpose of infrastructure is to mitigate risk, it also involves new risks as it comes to fruition. The article concludes with a series of suggestions and provocations to view the study of infrastructure in more contingent and paradoxical forms.