A bewildering variety of devices for communication from humans to computers now exists on the market. In this article, we propose a descriptive framework for analyzing the design space of these input devices. We begin with Buxton's (1983) idea that input devices are transducers of physical properties in one, two, or three dimensions. Following Mackinlay's semantic analysis of the design space for graphical presentations, we extend this idea to more comprehensive descriptions of physical properties, space, and transducer mappings. In our reformulation, input devices are transducers of any combination of linear and rotary, absolute and relative, position and force, in any of the six spatial degrees of freedom. Simple input devices are described in terms of semantic mappings from the transducers of physical properties into the parameters of the applications. One of these mappings, the resolution function, allows us to describe the range of possibilities from continuous devices to discrete devices, including possibilities in between. Complex input controls are described in terms of hierarchical families of generic devices and in terms of composition operators on simpler devices. The description that emerges is used to produce a new taxonomy of input devices. The taxonomy is compared with previous taxonomies of Foley, Wallace, and Chan (1984) and of Buxton (1983) by reclassifying the devices previously analyzed by these authors. The descriptive techniques are further applied to the design of complex mouse-based virtual input controls for simulated three-dimensional (3D) egocentric motion. One result is the design of a new virtual egocentric motion control.