We propose compact and efficient tetrahedral mesh representations to improve the ray-tracing performance. We reorder tetrahedral mesh data using a space-filling curve to improve cache locality. Most importantly, we propose efficient ray traversal algorithms. We provide details of the regular ray tracing operations on tetrahedral meshes and the Graphics Processing Unit (GPU) implementation of our traversal method. We demonstrate our findings through a set of comprehensive experiments. Our method outperforms existing tetrahedral mesh-based traversal methods and yields comparable results to the traversal methods based on the state-of-the-art acceleration structures such as k-dimensional (k-d) tree and Bounding Volume Hierarchy (BVH) in terms of speed. Storage-wise, our method uses less memory than its tetrahedral mesh-based counterparts, thus allowing larger scenes to be rendered on the GPU. We also describe additional applications of our technique specifically for volume rendering, two-level hybrid acceleration structures for animation purposes, and point queries in two-dimensional (2-D) and three-dimensional (3-D) triangulations. Finally, we present a practical method to tetrahedralize very large scenes.