The most cost-effective method to improve the damping of low frequency electromechanical oscillations in interconnected power systems is the use of Power System Stabilizers (PSS), which act as supplementary controllers in the generator excitation system. In general, the performance of a power system stabilizer depends on the proper tuning of its parameters, to ensure a positive contribution to the small signal stability of the power system, without negatively impacting its transient stability. This paper will discuss the different roles of the excitation system automatic voltage regulator and the power system stabilizer in improving the transient stability and the oscillatory stability of the power system. The focus of the paper will be on the tuning methodology for power system stabilizers, which can ensure a robust performance of the PSS over a wide range of frequencies and operating conditions. In addition, mathematical optimization techniques will be introduced into the tuning process to improve the efficiency and accuracy of the tuning process.