Using flexible AC transmission system (FACTS) devices in power systems while adhering to some equality and inequality constraints, researchers around the world sought to address this issue with the objectives of improving the voltage profile, reducing power losses in transmission lines, and increasing system reliability and safety. The recent development of FACTS controllers opens up new perspectives for safer and more efficient operation of electrical power networks by continuous and rapid action on power systems parameters, such as phase angle shifting, voltage injection and line impedance compensation. Thus, an improvement on voltage profile and enhancement of power transfer capability can be obtained. It is for that, the idea behind the FACTS concept is to enable the transmission system to be an active element in increasing the flexibility of power transfer requirements and in securing stability of integrated power system. It may also be effective in transient stability improvement, power oscillations damping and balancing power flow in parallel lines. The primary issue that has significantly piqued the interest of a number of researchers working in this field is the FACTS optimization problem, which involves determining the optimal type, location, and size of FACTS devices in electrical power systems. For solving this mixed integer, nonlinear and non-convex optimization problem, this paper provides an in-depth and comprehensive review of the various optimization techniques covered in published works in the field. In this review, a classification of optimization techniques in five main groups that are widely used, such as classical optimization techniques or conventional optimization approaches, Meta heuristic methods, analytic methods or sensitive index methods and mixed or hybrid methods, is summarized. In addition, a performance descriptions and comparison of these different optimization techniques are discussed in this study. Finally, some advice is offered for future research in this field.