In many cases, Tangible User Interfaces allow the manipulation of digital content with physical objects recognized by an interactive tabletop. Usually, such tangible objects are made of opaque wood or synthetic materials, thereby occluding the display. In this paper, we systematically investigate the promising potential of tangibles entirely made of transparent or translucent materials. Besides visualizing content directly below a manipulable tangible, transparent objects also facilitate direct touch interaction with the content below, dynamic illumination and glowing effects. We propose a comprehensive design space for transparent tangibles on tabletops based on a thorough review of existing work. By reporting on our own experiments and prototypes, we address several gaps in this design space, regarding aspects of both interaction and visualization. These include the illumination of tangibles as well as the precise input with transparent tangibles for which we also present the promising results of an initial user study. Finally, benefits and shortcomings of transparent tangibles are discussed and resulting design considerations are presented.