We present an approach to designing input devices that focuses on the structure of materials. We explore and visualize how a material reacts under manipulation, and harness the material’s properties to design new movement sensors. Two benefits spring out of this approach. One, simpler sensing emerges from making use of existing structure in the material. Two, by working with the natural structure of the material, we create input devices with readily recognizable affordances. We present six projects using this approach. We use the natural structure (coordination) of the human body to enable a mapping from five clothing-mounted accelerometers to high-quality motion capture data, creating a low-cost performance animation system. We design silicone input devices with embedded texture allowing single-camera tracking. We study squishable, conformable materials such as foam and silicone, and create a vocabulary of unit structures (shaped cuts in the material) for harnessing patterns of compression/tension to capture particular manipulations. We use this vocabulary to build soft sensing skeletons for stuffed animals, making foam cores with e-textile versions of our unit structures. We also use this vocabulary to design a tongue input device for a collaboration with Disney Imagineering. Finally, we rethink this vocabulary and apply it to capturing, using air pressure sensors, manipulations of hollow 3D-printed rubber shapes, and 3D-print several interactive robots incorporating the new vocabulary.