In recent decades, the rapid rise in electricity demand has compelled transmission and distribution systems to operate at almost their maximum capacity. This can pose numerous technical challenges such as excessive power losses, voltage and transient instabilities, as well as reduced power quality and reliability. Employment of Flexible Alternating Current Transmission System (FACTS) devices can be an effective approach to obviate such challenges and reinforce the power system functionality. Nevertheless, FACTS devices require a high initial investment, and hence their optimal allocation in terms of various aspects such as type, size and location is of utmost importance. This cannot be achieved without the deployment of optimization techniques. The aim of this paper is to provide a comprehensive review of the existing proposals for the enhancement of power system performance adopting FACTS devices. Adhering to that, an in-depth analysis is carried out, in which the most pertinent options are classified into specific groups based on their optimization objectives. Finally, a comparative analysis is accomplished in which the main attributes and drawbacks of each optimization technique are presented.