Shape sensing technology based on optical fibers is a new research direction in the field of optical fiber sensing. In recent years, fiber shape sensors have used several optical fibers with a specific spatial arrangement to measure the position and shape of the fiber or the connected objects. Because it is free from electromagnetic interference, easy to integrate, and has high accuracy in shape measurement, it can be applied to minimally invasive medical interventional catheter position tracking, critical structural shape measurement in the aerospace field, long-distance pipelines, and cable deformation monitoring. This paper discusses the application of fiber shape sensing technology in related fields. It systematically reviews the latest domestic and international research progress on this technology, as well as its key aspects. A detailed introduction is presented, and the major limiting factors and sources of errors in optical fiber shape sensing are summarized.