Optical fiber shape sensing technology is an innovative technological solution for 3D morphological recovery such as flexible body morphological measurement, real-time morphological tracking of optical cables, and real-time tracking of medical interventional needle trajectories, and so on. Optical fiber shape sensor taking optical fiber as the sensing components. The sensor has many advantages such as simple structure, easy embedding and installation, measurement without visual contact, corrosion resistance, and anti-electromagnetic interference, etc. It is suitable for large-scale structure morphology measurement in complex environments such as underwater and underground. In recent years, fiber optic shape sensors have received increasing attention. In this paper, the latest research progress of optical fiber shape sensing technology was reviewed. Taking one demension optical fiber curvature sensor, omnidirectional optical curvature fiber sensor and spatial shape sensor as clues, the current research status of the sensors at each stage and the challenges faced by them were introduced.