Devices made from stretchable electronic materials could be incorporated into clothing or attached directly to the body. Such materials have typically been prepared by engineering conventional rigid materials such as silicon, rather than by developing new materials. Here, we report a class of wearable and stretchable devices fabricated from thin films of aligned single-walled carbon nanotubes. When stretched, the nanotube films fracture into gaps and islands, and bundles bridging the gaps. This mechanism allows the films to act as strain sensors capable of measuring strains up to 280% (50 times more than conventional metal strain gauges), with high durability, fast response and low creep. We assembled the carbon-nanotube sensors on stockings, bandages and gloves to fabricate devices that can detect different types of human motion, including movement, typing, breathing and speech.