The inference of complete three-dimensional （3D） shape and semantic scene information from partial observations is crucial for various applications， such as autonomous driving， robotic vision， and metaverse ecosystem construction. Research on 3D completion has primarily focused on 3D-shape， 3D-scene， and 3D-semantic scene completion. In this paper， we systematically summarize and analyze recent relevant studies concerning these 3D completion tasks. First， for 3D-shape completion， the research progress is reviewed from two aspects： traditional shape completion and deep learning-based shape completion. Second， for 3D-scene completion， the research progress is reviewed from two aspects： the scene completion method based on model fitting and the scene completion method based on a generative approach. For 3D-semantic scene completion， the coupling characteristics between the two tasks of scene completion and semantic segmentation are analyzed， and the research progress is reviewed from three aspects： the depth map-based semantic scene completion method， the depth map-based semantic scene completion method with color images， and the point cloud-based semantic scene completion method， according to the different forms of input data. Finally， we analyze the current problems and future development trends of 3D completion tasks， aiming to provide a reference for related studies in this emerging field in 3D vision.