Perceiving the material properties of objects through touch is generally superior to the perception of shape. We review major material properties accessible through haptic interaction, along with theoretical accounts of the underlying perceptual processes. These include roughness, friction, compliance, and thermal properties. Subsequently, we describe algorithms that have been used to render these same material properties on haptic devices. We then point to applications that have capitalized on the accessibility of material through touch, including tactile displays, simulation of mechanical mechanisms in the automobile, and medical training simulators.