Past research on shape displays has primarily focused on rendering content and user interface elements through shape output, with less emphasis on dynamically changing UIs. We propose utilizing shape displays in three different ways to mediate interaction: to facilitate by providing dynamic physical affordances through shape change, to restrict by guiding users with dynamic physical constraints, and to manipulate by actuating physical objects. We outline potential interaction techniques and introduce Dynamic Physical Affordances and Constraints with our inFORM system, built on top of a state-of-the-art shape display, which provides for variable stiffness rendering and real-time user input through direct touch and tangible interaction. A set of motivating examples demonstrates how dynamic affordances, constraints and object actuation can create novel interaction possibilities.