I will discuss research in the RE Touch Lab (www.re-touch-lab) at UC Santa Barbara.  Our research addresses longstanding challenges in haptics, including the scientific understanding of the sense of touch, and the engineering of haptic display technologies - analogs of video displays for the sense of touch.  I will describe the origins of these challenges in human perception, in physics at multiple length and time scales, and in device engineering.  I will show how our research group is addressing engineering challenges in haptics by characterizing and exploiting physical mechanisms of energy transport, through computational tools, and through the engineering of new material systems and technologies.