Over the last decade, considerable research interest has peaked in realizing an efficient Terahertz (THz) waveguide for potential applications in imaging, sensing, and communications applications. Two of the promising candidates are the two-wire waveguide and the parallel-plate waveguide (PPWG). I present theoretical and experimental evidence that show that the two-wire waveguide supports low loss terahertz pulse propagation, and illustrate that the mode pattern at the end of the waveguide resembles that of a dipole. In comparison to the weakly guided Sommerfeld wave of a single wire waveguide, this two-wire structure exhibits much lower bending losses. I also observe that a commercial 300-Ohm two-wire TV-antenna cable can be used for guiding frequency components of up to 0.2 THz, although these cables are generally designed to operate only up to about 800 MHz. The parallel-plate waveguide is another promising candidate that would make an efficient THz waveguide, since it has relatively low Ohmic losses. The transverse electromagnetic mode (TEM) of this waveguide has been generally preferred since it has no cutoff frequency, and therefore no group velocity dispersion. Utilizing this TEM mode, I study the reflection of THz radiation at the end of a PPWG, due to the impedance mismatch between the propagating transverse-electromagnetic mode and the free-space background. I find that for a PPWG with uniformly spaced plates, the reflection coefficient at the output face increases as the plate separation decreases, consistent with predictions by early low frequency ray optical theory. I observe this same trend in tapered PPWGs, when the input separation is fixed, and the output separation is varied. In another study, I investigate how to minimize diffraction losses in PPWGs by using plates with slightly concave surfaces. Using a simple “bouncing plane wave” analysis, I demonstrate how to determine an ideal radius of curvature for a waveguide operating at a given THz frequency. I perform a detailed experimental and simulation study that illustrates, for a waveguide with a plate separation of 1 cm, one can inhibit the diffraction around a frequency of 0.1 THz, when the surface has a curvature of 6.7 cm. Using much longer PPWGs (about 170cm), I reliably measure the overall losses in a PPWG with a radius of curvature of R=6.7 cm, and find it to be less than 1db/m around the design frequency (of 0.1 THz). This is very close to the lowest achieved loss to date with any terahertz waveguide.