The attacks suffered by France in January and November 2015, and then in the course of 2016, especially the Nice attack, provoked intense online activity both during the events and in the months that followed. The digital traces left by this reactivity and reactions to events gave rise, from the very first days and even hours after the attacks, to a 'real-time' institutional archiving by the National Library of France (Bibliothèque nationale de France, BnF) and the National Audiovisual Institute (Institut national de l'audiovisuel, Ina). The results amount to millions of archived tweets and URLs. This article seeks to highlight some of the most significant issues raised by these relatively unedited corpora, from collection to exploitation, online stream of data to its mediation and re-composition. Indeed, Web archiving practices in times of emergency and crises are significant, almost emblematic, loci to explore the human and technical agencies, and the complex temporalities, of 'born-digital' heritage. The cases examined here emphasize the way these "emergency collections" challenge the perimeters and the very nature of Web archives as part of our digital and societal heritage, and the guiding visions of its governance and mission. Finally, the present analysis emphasizes the need for a careful contextualisation of the design process-both of original web pages or tweets and of their archived images-and of the tools deployed to collect, retrieve and analyse them.