I describe a variety of spiral tilings of triangles in which adjacent tiles scale by a constant factor. Different ways of mating smaller triangles to larger triangles are analyzed, and examples are given with single and multiple spiral arms. The different possibilities are explored methodically, revealing many tilings not reported previously. These tilings contain a singular point at their center where the triangles become infinitesimally small. In addition to their inherent beauty, these constructions can be used in mathematical art, sculpture, and architecture.