The function of borders has changed. In addition to marking the boundaries of a territory and the sovereignty of nation-states, “bordering” has become an infrastructural project that is applied in various situations. This article looks into three situations of infrastructural bordering: namely, (1) externalization of border control, (2) disaster displacement, and (3) health security. These situations indicate that infrastructural bordering takes place in a hybrid world. As infrastructures, borders are intermingled with technologies of all sorts, varying from large databases and visual surveillance techniques to biometric applications and the creation of smart borders. These technologies affect the place of borders by placing them outward and inward of countries, as well as the temporalities of border control by connecting analyses of past and future movements to the present. Border infrastructures not only relate to technology but also connect to “nature” in specific ways—that is, to weather conditions, the environment, climate change, disasters, and viruses in the context of health security. The article suggests that in these situations, borders conduct acts of “infrastructural isolation” and “infrastructural circulation” that construct distinct but connected spheres that allow for the application of specific measures for movable configurations of humans and nonhumans. Bordering, in that sense, consists of a meticulous interplay between “circulation” and “isolation.” The article is part of the Global Perspectives, Media and Communication special issue on “Media, Migration, and Nationalism,” guest-edited by Koen Leurs and Tomohisa Hirata.