During the last two decades, the emergence of fresh categories within new media art has posed unprecedented challenges to museums, motivating the creation of new institutions specifically designed to house and display works of this type. Therefore, digital and Internet art have configured an interesting field for architectural research. Frequently, the architecture of these new museums has revealed utopian visions that derive from profound contradictions between the intangible world of communication technology and the conventional requirements of physical spaces. Just as in previous periods of art history, some of the most ground-breaking projects did not end up as finished buildings, either because their construction would be too expensive and technically problematic, or just because they were deliberately conceived as virtual spaces. However, and surprisingly enough, even these web-specific museums sometimes proved to be too ambitious or ahead of their time. In this scenario, and drawing on a set of emblematic projects, this paper seeks to discuss a topical question: how can museum architecture deal with the intangible, unstable and ubiquitous condition of digital art?