In this presentation, we'll take a quick visual, metric, and axiomatic tour of several non-Euclidean geometries (including taxi-cab geometry, hyperbolic geometry, and Minkowski space-time) using The Geometer's Sketchpad. We'll discuss their pedagogic motivation and potential treatment at an upper-secondary or early undergraduate level, and explore a developmental trajectory leading to the astonishing, pleasing, and accessible results in hyperbolic tessellation. While this tutorial will not involve hands-on computers, participants will be given materials and technology allowing them to explore and introduce many non-Euclidean geometry microworlds that have been developed in Sketchpad.