The use of FACTS devices in power systems has become increasingly popular in recent years, as they offer a number of benefits, including improved voltage profile, reduced power losses, and increased system reliability and safety. However, determining the optimal type, location, and size of FACTS devices can be a challenging optimization problem, as it involves mixed integer, nonlinear, and nonconvex constraints. To address this issue, researchers have applied various optimization techniques to determine the optimal configuration of FACTS devices in power systems. The paper provides an in-depth and comprehensive review of the various optimization techniques that have been used in published works in this field. The review classifies the optimization techniques into four main groups: classical optimization techniques, metaheuristic methods, analytic methods, and mixed or hybrid methods. Classical optimization techniques are conventional optimization approaches that are widely used in optimization problems. Metaheuristic methods are stochastic search algorithms that can be effective for nonconvex constraints. Analytic methods involve sensitivity analysis and gradient-based optimization techniques. Mixed or hybrid methods combine different optimization techniques to improve the solution quality. The paper also provides a performance comparison of these different optimization techniques, which can be useful in selecting an appropriate method for a specific problem. Finally, the paper offers some advice for future research in this field, such as developing new optimization techniques that can handle the complexity of the optimization problem and incorporating uncertainties into the optimization model. Overall, the paper provides a valuable resource for researchers and practitioners in the field of power systems optimization, as it summarizes the various optimization techniques that have been used to solve the FACTS optimization problem and provides insights into their performance and applicability.