After almost a decade of relentless development, pervasive urban displays have fragmented into a diversity of approaches with radically distinct characteristics in terms of how mobile they are, as well as the materials they are made of. In this article, we investigate such a diversity in terms of the relationships between key conceptual entities of pervasive urban displays, namely the displayed content, the enabling display technology and the surrounding physical environment. First, we propose a taxonomy for pervasive urban displays through two dimensions: increasing levels of physical integration of content into the surrounding environment (attached, blended, physicalised), and increasing levels of mobility of the display technology within the environment (fixed, portable, self-moving). We extend this taxonomy through looking at the relationship between content and display technology from a conceptual lens and present two categories, namely Screens and Printers. We then provide a classification of current approaches to the design of pervasive displays along these two dimensions and categories, and introduce a new class of pervasive display, which we call pulverised urban displays (PUDs). These displays represent content in a physical form, entangled with the built and natural environment which are capable of an autonomous change to their position. Drawing on urban robotic devices and their capability to sense and manipulate the environment or act as a display itself, we present examples of PUDs. Finally, this article concludes with challenges for designing self-moving robotic and pulverised urban displays.