Modern power system networks are complex and subjected to several uncertainties. Due to the complexity and uncertainties involved in power system operation, the networks are prone to instabilities. Rotor-angle instability is one such issue that, if not addressed properly, may lead to system collapse. A power system stabilizer (PSS) is primarily a power oscillation damping (POD) controller used to dampen power oscillations, thereby improving rotor angle stability. The proper design of PSSs is a challenging task and is essential for the secure and reliable operation of power systems. In the past, many power system instability events occurred, resulting in cascading failures and even blackouts. In the literature, several methods are proposed for the efficient design of PSSs or POD controllers. In this contribution, a recent review on the design of PSS is presented, along with challenges and the future scope of research in this field. On the basis of this review, it can be concluded that there is ample scope for designing PSS in a more efficient and robust manner, considering several uncertainties that may occur during the operation of modern power systems.