Human-computer interface devices are rigid, and afford little or no opportunity for end-user adaptation. This thesis proposes that valuable new interaction possibilities can be generated through the development of user interface hardware that is increasingly flexible, and allows end-users to physically shape, construct and modify physical interfaces for interactive systems. The work is centred around the development of a novel platform for flexible user interfaces (called VoodooIO) that allows end-users to compose and adapt physical control structures in a manner that is both versatile and simple to use. VoodooIO has two main physical elements: a pliable material (called the substrate), and a set of physical user interface controls, which can be arranged on the surface of the substrate.The substrate can be shaped, applied to existing surfaces, attached to objects and placed on walls and furniture to designate interface areas on which users can spatially lay out controls. From a technical perspective, the design of VoodooIO is based on a novel architecture for user interfaces as networks of controls, where each control is implemented as a network node with physical input and output capabilities. The architecture overcomes the inflexibility that is usually imposed by hard-wired circuitry in traditional interface devices, by enabling individual control elements that can be connected and disconnected ad hoc from a shared network bus. The architecture includes support for a wide and extensible range of control types; fast control identification and presence detection, and an application-level interface that abstracts from low level implementation details and network management processes. The concrete contributions to the field of human-computer interaction include a motivation for the development of flexible physical interfaces, a fully working example of such a technology, and insights gathered from its application and study.