Since 2014, millions of refugees and migrants have arrived at the borders of Europe. This article argues that, in making their way to safe spaces, refugees rely not only on a physical but increasingly also digital infrastructure of movement. Social media, mobile devices, and similar digitally networked technologies comprise this infrastructure of “digital passages”—sociotechnical spaces of flows in which refugees, smugglers, governments, and corporations interact with each other and with new technologies. At the same time, a digital infrastructure for movement can just as easily be leveraged for surveillance and control. European border policies, in particular, instantiate digital controls over refugee movement and identity. We review the actors, technologies, and policies of movement and control in the EU context and argue that scholars, policymakers, and the tech community alike should pay heed to the ethics of the use of new technologies in refugee and migration flows.