Impermanence and fragility have become the defining conditions of the digital age. Technologies that were ubiquitous barely a decade ago, like floppy disks, now look like archaeological relics. It takes only a few years, if not months, before software environments are replaced by newer versions, often with limited backward compatibility. At the same time, digital technologies rely on hardware that has short life expectancy. The radical obsolescence of this new digital register raises a number of important questions. How are we going to prevent the fragile memories of contemporary digital cultures from receding into oblivion? This essay answers this question by looking at one of the institutions in which the problems associated with digital fragility are most especially felt, the Museum of Modern Art (MoMA), and by exploring the ontological displacements that digital objects are operating at the heart of the museum.