As a novel class of mobile devices with rich interaction capabilities we introduce tPads -- transparent display tablets. tPads are the result of a systematic design investigation into the ways and benefits of interacting with transparent mobiles which goes beyond traditional mobile interactions and augmented reality (AR) applications. Through a user-centered design process we explored interaction techniques for transparent-display mobiles and classified them into four categories: overlay, dual display & input, surface capture and model-based interactions. We investigated the technical feasibility of such interactions by designing and building two touch-enabled semi-transparent tablets called tPads and a range of tPad applications. Further, a user study shows that tPad interactions applied to everyday mobile tasks (application switching and image capture) outperform current mobile interactions and were preferred by users. Our hands-on design process and experimental evaluation demonstrate that transparent displays provide valuable interaction opportunities for mobile devices.