The quasi-distributed fiber Bragg grating (FBG) shape sensor measures the position and shape of an object connected to an optical fiber by combining multiple FBGs using wavelength division multiplexing technology. Characterized by immunity to electromagnetic interference, ease of integration, corrosion resistance, and strong wavelength selectivity, FBG has high sensitivity to the three-dimensional (3D) shape changes of beams, panels, and skins. Thus, it is reliable for monitoring the health of critical structures in aerospace and healthcare fields. In this study, the domestic and international research progress on 3D shape reconstruction algorithms based on quasi-distributed FBG is reviewed. The influence of FBG layout density and temperature on the reconstruction effect of four algorithms is discussed. The advantages and disadvantages of each algorithm as well as the suitable reconstruction objects are summarized, and future directions of improvement are outlined.