Underwater robots and key technologies for operation control have been reviewed in this article. The Underwater Vehicle-Manipulator System (UVMS) has become increasingly important in exploring and utilizing marine resources. However, the underwater environment presents significant challenges for control, navigation, and communication. These challenges have driven the continuous development of related technologies and made the UVMS even more attractive. The article first reviews the development status of the UVMS and discusses current limitations and future directions. It then reviews dynamic and hydrodynamic modeling methods, analyzes the principles, advantages, and disadvantages of various approaches, and discusses two key technologies for operation control: underwater positioning and navigation technologies and vehicle-manipulator coordinated control approaches. Finally, a reasonable prospect for the future development of UVMS is given. The development of UVMS has a long history, with early examples dating back to the 16th century. Over the past decades, UVMS have evolved from remotely operated vehicles (ROVs) to more autonomous systems. The United States, Japan, South Korea, and Europe have made significant contributions to the development of UVMS. The latest UVMS can operate at depths of up to 6,000 meters and are equipped with advanced sensors and manipulators. The UVMS is classified based on weight, size, operation mode, and propulsion method. The key technologies of the UVMS include dynamic modeling, underwater positioning and navigation, motion control, and vehicle-manipulator coordinated control. Dynamic modeling is essential for structural optimization, simulation, and controller design. Various methods, such as the Newton-Euler method, Quasi-Lagrange method, and data-driven methods, have been used for dynamic modeling. Hydrodynamic modeling is also important, as it affects the accuracy and stability of underwater operations. Current methods for obtaining hydrodynamic coefficients include empirical formulas, restraint tests, numerical simulation analysis, and motion parameter identification. Underwater positioning and navigation are challenging due to the highly unstructured and nonlinear nature of the underwater environment. Vision-based methods, acoustic-based methods, and multisensory fusion methods have been developed to improve positioning accuracy. Acoustic-based methods are widely used due to their ability to provide precise positioning in underwater environments. Multisensory fusion methods combine data from multiple sensors to enhance positioning accuracy and robustness. Autonomous operation control technology is crucial for UVMS. Motion control ensures precise positioning and trajectory tracking in unstructured environments. Vehicle-manipulator coordinated control is also important for autonomous operations. Various control methods, such as Sliding Mode Control (SMC), Model Predictive Control (MPC), and Reinforcement Learning (RL), have been developed for motion control. Task-priority methods are used for vehicle-manipulator coordinated control. In summary, the UVMS has made significant progress in recent years, with various technologies being developed to improve its performance. However, there are still challenges that need to be addressed, such as improving autonomous operation capability and reducing the cost of UVMS.Underwater robots and key technologies for operation control have been reviewed in this article. The Underwater Vehicle-Manipulator System (UVMS) has become increasingly important in exploring and utilizing marine resources. However, the underwater environment presents significant challenges for control, navigation, and communication. These challenges have driven the continuous development of related technologies and made the UVMS even more attractive. The article first reviews the development status of the UVMS and discusses current limitations and future directions. It then reviews dynamic and hydrodynamic modeling methods, analyzes the principles, advantages, and disadvantages of various approaches, and discusses two key technologies for operation control: underwater positioning and navigation technologies and vehicle-manipulator coordinated control approaches. Finally, a reasonable prospect for the future development of UVMS is given. The development of UVMS has a long history, with early examples dating back to the 16th century. Over the past decades, UVMS have evolved from remotely operated vehicles (ROVs) to more autonomous systems. The United States, Japan, South Korea, and Europe have made significant contributions to the development of UVMS. The latest UVMS can operate at depths of up to 6,000 meters and are equipped with advanced sensors and manipulators. The UVMS is classified based on weight, size, operation mode, and propulsion method. The key technologies of the UVMS include dynamic modeling, underwater positioning and navigation, motion control, and vehicle-manipulator coordinated control. Dynamic modeling is essential for structural optimization, simulation, and controller design. Various methods, such as the Newton-Euler method, Quasi-Lagrange method, and data-driven methods, have been used for dynamic modeling. Hydrodynamic modeling is also important, as it affects the accuracy and stability of underwater operations. Current methods for obtaining hydrodynamic coefficients include empirical formulas, restraint tests, numerical simulation analysis, and motion parameter identification. Underwater positioning and navigation are challenging due to the highly unstructured and nonlinear nature of the underwater environment. Vision-based methods, acoustic-based methods, and multisensory fusion methods have been developed to improve positioning accuracy. Acoustic-based methods are widely used due to their ability to provide precise positioning in underwater environments. Multisensory fusion methods combine data from multiple sensors to enhance positioning accuracy and robustness. Autonomous operation control technology is crucial for UVMS. Motion control ensures precise positioning and trajectory tracking in unstructured environments. Vehicle-manipulator coordinated control is also important for autonomous operations. Various control methods, such as Sliding Mode Control (SMC), Model Predictive Control (MPC), and Reinforcement Learning (RL), have been developed for motion control. Task-priority methods are used for vehicle-manipulator coordinated control. In summary, the UVMS has made significant progress in recent years, with various technologies being developed to improve its performance. However, there are still challenges that need to be addressed, such as improving autonomous operation capability and reducing the cost of UVMS.