Lying between optical and microwave ranges, the terahertz band in the electromagnetic spectrum is attracting increased attention. Optical fibers are essential for developing the full potential of complex terahertz systems. In this manuscript, we review the optimal materials, the guiding mechanisms, the fabrication methodologies, the characterization methods and the applications of such terahertz waveguides. We examine various optical fiber types including tube fibers, solid core fiber, hollow-core photonic bandgap, anti-resonant fibers, porous-core fibers, metamaterial-based fibers, and their guiding mechanisms. The optimal materials for terahertz applications are discussed. The past and present trends of fabrication methods, including drilling, stacking, extrusion and 3D printing, are elaborated. Fiber characterization methods including different optics for terahertz time-domain spectroscopy (THz-TDS) setups are reviewed and application areas including short-distance data transmission, imaging, sensing, and spectroscopy are discussed.