Achieving low-loss and flexible transmission of terahertz wave is the key approach to develop light and portable terahertz equipment. Research progress of terahertz fiber waveguide technology is overviewed. The whole progress is divided into 3 stages described as selection and exploitation of original materials, design and fabrication of pure materials, design and fabrication of drawn meta-material. Then the achievements, advantages and disadvantages, and applications of these stages are analyzed. Finally, it is prospected that the drawn meta-material will be a novel research direction, and the high-transmission, flexible and low-cost terahertz fiber waveguide is expected to be fabricated in the future.