The paper provides a comprehensive survey of control allocation algorithms for over-actuated mechanical systems, which are systems with more effectors than necessary to achieve the desired motion control objectives. The control allocation process involves three levels: a high-level motion control algorithm that commands virtual control efforts, a control allocation algorithm that coordinates the effectors to produce these efforts, and low-level control algorithms that manage individual effectors via their actuators. The paper emphasizes the modular design of control allocation, allowing the high-level motion control algorithm to be designed without detailed knowledge of the effectors and actuators. Key issues such as input saturation, rate constraints, fault tolerance, and secondary objectives like power efficiency are handled within the control allocation algorithm. The survey classifies control allocation algorithms into two main categories: those based on linear and nonlinear models. Linear models are simpler and can be solved explicitly using numerical linear algebra, while nonlinear models require iterative numerical optimization procedures. The paper discusses various optimization-based design approaches, including explicit solutions for linear models and more complex formulations for nonlinear models. It also highlights the importance of handling physical constraints, operational constraints, and other objectives within the control allocation framework. The paper reviews recent developments in control allocation, particularly in the automotive and mechatronics industries, where nonlinear approaches have gained attention. It covers different methods for constrained control allocation, such as the redistributed pseudo-inverse method, daisy chaining, direct allocation, and error minimization using linear and quadratic programming. The paper also explores the integration of dynamics and fault tolerance in control allocation, including adaptive solutions for unknown time-varying parameters and dynamic control allocation approaches. Finally, the paper discusses the application of model predictive control (MPC) in control allocation, which can handle actuator dynamics and constraints more effectively than static control allocation methods. The paper concludes with perspectives on new applications and theoretical challenges in control allocation.The paper provides a comprehensive survey of control allocation algorithms for over-actuated mechanical systems, which are systems with more effectors than necessary to achieve the desired motion control objectives. The control allocation process involves three levels: a high-level motion control algorithm that commands virtual control efforts, a control allocation algorithm that coordinates the effectors to produce these efforts, and low-level control algorithms that manage individual effectors via their actuators. The paper emphasizes the modular design of control allocation, allowing the high-level motion control algorithm to be designed without detailed knowledge of the effectors and actuators. Key issues such as input saturation, rate constraints, fault tolerance, and secondary objectives like power efficiency are handled within the control allocation algorithm. The survey classifies control allocation algorithms into two main categories: those based on linear and nonlinear models. Linear models are simpler and can be solved explicitly using numerical linear algebra, while nonlinear models require iterative numerical optimization procedures. The paper discusses various optimization-based design approaches, including explicit solutions for linear models and more complex formulations for nonlinear models. It also highlights the importance of handling physical constraints, operational constraints, and other objectives within the control allocation framework. The paper reviews recent developments in control allocation, particularly in the automotive and mechatronics industries, where nonlinear approaches have gained attention. It covers different methods for constrained control allocation, such as the redistributed pseudo-inverse method, daisy chaining, direct allocation, and error minimization using linear and quadratic programming. The paper also explores the integration of dynamics and fault tolerance in control allocation, including adaptive solutions for unknown time-varying parameters and dynamic control allocation approaches. Finally, the paper discusses the application of model predictive control (MPC) in control allocation, which can handle actuator dynamics and constraints more effectively than static control allocation methods. The paper concludes with perspectives on new applications and theoretical challenges in control allocation.