We describe a new architecture composed of software and hardware for displaying stereoscopic images over a horizontal surface. It works as a ``Virtual Table and Teleporter'', in the sense that virtual objects depicted over a table have the appearance of real objects. This system can be used for visualization and interaction. We propose two basic configurations: the Virtual Table, consisting of a single display surface, and the Virtual Teleporter, consisting of a pair of tables for image capture and display. The Virtual Table displays either 3D computer generated images or previously captured stereoscopic video and can be used for interactive applications. The Virtual Teleporter captures and transmits stereoscopic video from one table to the other and can be used for telepresence applications. In both configurations the images are properly deformed and displayed for horizontal 3D stereo. In the Virtual Teleporter two cameras are pointed to the first table, capturing a stereoscopic image pair. These images are shown on the second table that is, in fact, a stereoscopic display positioned horizontally. Many applications can benefit from this technology such as virtual reality, games, teleconferencing, and distance learning. We present some interactive applications that we developed using this architecture.