Several classes of non-planar metallic and dielectric waveguides have been proposed in the literature for guidance of terahertz (THz) or Tray radiation. In this review, we focus on the development of dielectric waveguides, in the THz regime, with reduced loss and dispersion. First, we examine different THz spectroscopy configurations and fundamental equations employed for characterization of THz waveguides. Then we divide THz dielectric waveguides into three classes: solid-core, hollow-core, and porous-core waveguides. The guiding mechanism, fabrication steps, measured loss, and dispersion are presented for the waveguides in each class in chronological order. The goal of this review is to compare and contrast the current solutions for guiding THz radiation.