This document reviews 59 studies on optimization algorithms for determining the optimal placement of flexible AC transmission system (FACTS) controllers. It categorizes the algorithms into analytical optimization techniques using sensitivity analysis, metaheuristic optimization techniques including evolutionary algorithms like genetic algorithm and differential evolution, and swarm-based algorithms like particle swarm optimization. It summarizes several studies applying these various techniques to test cases like IEEE 5, 14, 30 bus systems to optimally place FACTS controllers like thyristor controlled series compensator (TCSC), static VAR compensator (SVC), unified power flow controller (UPFC) with objectives of minimizing losses, improving voltage profile, enhancing security and loadability.