Incremental energy demand, environmental constraints, restrictions in the availability of energy resources, economic conditions, and political impact prompt the power sector toward deregulation. In addition to these impediments, electric power competition for power quality, reliability, availability, and cost forces utilities to maximize utilization of the existing infrastructure by flowing power on transmission lines near to their thermal limits. All these factors introduce problems related to power network stability, reliability, quality, congestion management, and security in restructured power systems. To overcome these problems, power-electronics-based FACTS devices are one of the beneficial solutions at present. In this review paper, the significant role of FACTS devices in restructured power networks and their technical benefits against various power system problems such as load frequency control, voltage stability, and congestion management will be presented. In addition, an extensive discussion about the comparison between different FACTS devices (series, shunt, and their combination) and comparison between various optimization techniques (classical, analytical, hybrid, and meta-heuristics) that support FACTS devices to achieve their respective benefits is presented in this paper. Generally, it is concluded that third-generation FACTS controllers are more popular to mitigate various power system problems (i.e., load frequency control, voltage stability, and congestion management). Moreover, a combination of multiple FACTS devices, with or without energy storage devices, is more beneficial compared to their individual usage. However, this is not commonly adopted in small power systems due to high installation or maintenance costs. Therefore, there is a trade-off between the selection and cost of FACTS devices to minimize the power system problems. Likewise, meta-heuristics and hybrid optimization techniques are commonly adopted to optimize FACTS devices due to their fast convergence, robustness, higher accuracy, and flexibility.