Automatic berthing is at the top level of ship autonomy; it is unwise and hasty to hand over the control initiative to the controller and the algorithm without the foundation of the maneuvering model. The berthing maneuver model predicts the ship responses to the steerage and external disturbances, and provides a foundation for the control algorithm. The modular MMG model is widely adopted in ship maneuverability studies. However, there are two ambiguous questions on berthing maneuver modeling: What are the similarities and differences between the conventional MMG maneuvering model and automatic berthing maneuvering model? How can an accurate automatic berthing maneuvering model be established? To answer these two questions, this paper firstly performs bibliometric analysis on automatic berthing, to discover the hot issues and emphasize the significance of maneuver modeling. It then demonstrates the similarities and differences between the conventional MMG maneuvering model and the automatic berthing maneuvering model. Furthermore, the berthing maneuver specifications and modeling procedures are explained in terms of the hydrodynamic forces on the hull, four-quadrant propulsion and steerage performances, external disturbances, and auxiliary devices. The conclusions of this work provide references for ship berthing mathematical modeling, auxiliary device utilization, berthing aid system improvement, and automatic berthing control studies.