Textiles have emerged as a promising class of materials for developing wearable robots that move and feel like everyday clothing. Textiles represent a favorable material platform for wearable robots due to their flexibility, low weight, breathability, and soft hand‐feel. Textiles also offer a unique level of programmability because of their inherent hierarchical nature, enabling researchers to modify and tune properties at several interdependent material scales. With these advantages and capabilities in mind, roboticists have begun to use textiles, not simply as substrates, but as functional components that program actuation and sensing. In parallel, materials scientists are developing new materials that respond to thermal, electrical, and hygroscopic stimuli by leveraging textile structures for function. Although textiles are one of humankind's oldest technologies, materials scientists and roboticists are just beginning to tap into their potential. This review provides a textile‐centric survey of the current state of the art in wearable robotic garments and highlights metrics that will guide materials development. Recent advances in textile materials for robotic components (i.e., as sensors, actuators, and integration components) are described with a focus on how these materials and technologies set the stage for wearable robots programmed at the material level.