Since the terahertz time-domain spectroscopy has been developed, there-has been great interest in the fabrication of terahertz waveguides, especially flexible and low-loss ones. Firstly, terahertz time-domain systems are introduced, and some shortcomings of conventional waveguides are summarized. Three working mechanisms of novel terahertz waveguides are presented in details, including reflection from metal surface, total reflection from the interface of two dielectric media and anti-resonant reflection. Characteristics of these waveguides are discussed. At last, some applications about flexible and low-loss terahertz waveguides are demonstrated, and continuing research is introduced.