To promote potential applications of terahertz (THz) technology, more advanced functional THz devices with high performance are needed, including modulators, polarizers, lenses, wave retarders, and antireflection coatings. This work summarizes recent progress in THz components built on functional materials including graphene, vanadium dioxide, and metamaterials. The key message is that, while the choice of materials used in such devices is important, the geometry in which they are employed also has a significant effect on the performance achieved. In particular, devices operating in total internal reflection geometry are reviewed, and it is explained how this geometry is able to be exploited to achieve a variety of THz devices with broadband operation.