In the past decade, multi-touch-sensitive interactive surfaces have transitioned from pure research prototypes in the lab, to commercial products with wide-spread adoption. One of the longer term visions of this research follows the idea of ubiquitous computing, where everyday surfaces in our environment are made interactive. However, most of current interfaces remain firmly tied to the traditional flat rectangular displays of the today’s computers and while they benefit from the directness and the ease of use, they are often not much more than touch-enabled standard desktop interfaces. In this paper, we argue for explorations that transcend the traditional notion of the flat display, and envision interfaces that are curved, three-dimensional, or that cross the boundary between the digital and physical world. In particular, we present two research directions that explore this idea: (a) exploring the threedimensional interaction space above the display and (b) enabling gestural and t...