The Atlas of Fantastic infrastructures deals with the characterization of architecture, media and digital infrastructure. In concrete terms, it deals with the materiality of buildings and the intangibility of data. While technical or functional studies often tend to “flatten” the multiplex phenomena, we speculatively propose four abstract prisms: 1) AFFAIR WITH PHANTOMS – who do we want to meet in a digitally mediated space, and what kind of conversation/activity will we have?; 2) PARA-DESIRE – where do our surreal desires live, and what are their strategies?; 3) MEDIATED SPACE CATALOGUE – what kinds of data, information, things, spaces and places are available in the world, and how our activities blend them?; 4) GIFTS OF THE GARDENS – how can an idea enter physical reality, and what are the pathways of such becomings? Buildings and projects by Toyo Ito, Philippe Rahm, Olafur Eliasson, Greg Lynn, MVRDV, Electroland, Troika, NOX, Rafael Lozano-Hemmer and others are examined.