In this chapter, I take as my point of departure the paradox that the undocumentedness of the undocumented, the paperlessness of the sans-papiers, is an absence—a lack—that perversely generates a veritable paper frenzy. While migration has been studied mainly through a spatial prism, the chapter contributes to the recent ‘temporal turn’ in migration studies by outlining a theoretical perspective for studying ‘documentation’ in light of the ‘temporal architectures’ that produce experiences of waiting, tempos and rhythms for migrants’ everyday lives, as well as affective relationships to a sense of the present and the future. The chapter locates the study in the historical context of the ‘welcoming crisis’ associated with the ‘Arab spring’ and ‘the long summer of migration’, characterized by the increasing illegalization and securitization of migration, the expansion of detention and deportation practices and the persistence of (post)colonial legacies. The chapter ends with a discussion of how we can think about the precarious struggles of undocumented migrants in facing intersecting economic, racial and gendered power structures. Whether individually, or by assembling together, migrants struggle both to make tolerable lives within, and to defy, the ‘condition of illegality’.