This paper surveys control allocation algorithms for over-actuated mechanical systems with redundant effectors and actuators. Control allocation is a key component of motion control algorithms, enabling the coordination of multiple effectors to achieve desired control objectives. The control allocation process typically involves three levels: high-level motion control, which computes a vector of virtual control efforts; a control allocation algorithm, which maps these virtual efforts to individual effectors; and low-level control algorithms, which control each effector via its actuators. The control allocation algorithm handles important issues such as input saturation, rate constraints, fault tolerance, and secondary objectives like power efficiency and wear minimization. Control allocation algorithms are classified into two main categories based on the use of linear or nonlinear models. Optimization-based design is a powerful approach due to the presence of physical constraints and secondary objectives. The simplest formulations allow explicit solutions using numerical linear algebra, while more complex formulations require iterative numerical optimization. The paper discusses various control allocation methods, including unconstrained linear control allocation, constrained linear control allocation, error minimization using linear programming, error minimization using quadratic programming, and explicit approaches to constrained error minimization. The paper also addresses the integration of dynamic actuator models and fault tolerance in control allocation. Dynamic control allocation methods, such as model predictive control (MPC), are used to handle actuator dynamics and constraints. The paper highlights the importance of considering actuator rate constraints and the use of optimization techniques to minimize allocation errors. It also discusses the use of nonlinear programming methods for control allocation, which are necessary for achieving desired performance in cases where linear models are insufficient. The paper concludes with perspectives on new applications and theoretical challenges in control allocation, emphasizing the importance of modular design and the need for robust and efficient algorithms that can handle a wide range of applications, including aerospace, maritime, automotive, and other industries.This paper surveys control allocation algorithms for over-actuated mechanical systems with redundant effectors and actuators. Control allocation is a key component of motion control algorithms, enabling the coordination of multiple effectors to achieve desired control objectives. The control allocation process typically involves three levels: high-level motion control, which computes a vector of virtual control efforts; a control allocation algorithm, which maps these virtual efforts to individual effectors; and low-level control algorithms, which control each effector via its actuators. The control allocation algorithm handles important issues such as input saturation, rate constraints, fault tolerance, and secondary objectives like power efficiency and wear minimization. Control allocation algorithms are classified into two main categories based on the use of linear or nonlinear models. Optimization-based design is a powerful approach due to the presence of physical constraints and secondary objectives. The simplest formulations allow explicit solutions using numerical linear algebra, while more complex formulations require iterative numerical optimization. The paper discusses various control allocation methods, including unconstrained linear control allocation, constrained linear control allocation, error minimization using linear programming, error minimization using quadratic programming, and explicit approaches to constrained error minimization. The paper also addresses the integration of dynamic actuator models and fault tolerance in control allocation. Dynamic control allocation methods, such as model predictive control (MPC), are used to handle actuator dynamics and constraints. The paper highlights the importance of considering actuator rate constraints and the use of optimization techniques to minimize allocation errors. It also discusses the use of nonlinear programming methods for control allocation, which are necessary for achieving desired performance in cases where linear models are insufficient. The paper concludes with perspectives on new applications and theoretical challenges in control allocation, emphasizing the importance of modular design and the need for robust and efficient algorithms that can handle a wide range of applications, including aerospace, maritime, automotive, and other industries.