We present a new type of actuatable display, called Tilt Displays, that provide visual feedback combined with multi-axis tilting and vertical actuation. Their ability to physically mutate provides users with an additional information channel that facilitates a range of new applications including collaboration and tangible entertainment while enhancing familiar applications such as terrain modelling by allowing 3D scenes to be rendered in a physical-3D manner. Through a mobile 3x3 custom built prototype, we examine the design space around Tilt Displays, categorise output modalities and conduct two user studies. The first, an exploratory study examines users' initial impressions of Tilt Displays and probes potential interactions and uses. The second takes a quantitative approach to understand interaction possibilities with such displays, resulting in the production of two user-defined gesture sets: one for manipulating the surface of the Tilt Display, the second for conducting everyday interactions.