Optical fibers are being widely utilized as radiation sensors and dosimeters. Benefiting from the rapidly growing optical fiber manufacturing and material engineering, advanced optical fibers have evolved significantly by using functional structures and materials, promoting their detection accuracy and usage scenarios as radiation sensors. This paper summarizes the current development of optical fiber-based radiation sensors. The sensing principles of both extrinsic and intrinsic optical fiber radiation sensors, including radiation-induced attenuation (RIA), radiation-induced luminescence (RIL), and fiber grating wavelength shifting (RI-GWS), were analyzed. The relevant advanced fiber materials and structures, including silica glass, doped silica glasses, polymers, fluorescent and scintillator materials, were also categorized and summarized based on their characteristics. The fabrication methods of intrinsic all-fiber radiation sensors were introduced, as well. Moreover, the applicable scenarios from medical dosimetry to industrial environmental monitoring were discussed. In the end, both challenges and perspectives of fiber-based radiation sensors and fiber-shaped radiation dosimeters were presented.