With the development of the energy structure of the power system, the characterization of the observed oscillation in the power system has steadily evolved. With the increasingly high penetration of distributed energy sources and power electronic devices, such as the photovoltaic, wind power and charging pile, the basic mechanism, frequency ranges and propagation of oscillation would become more dynamic and complex. Therefore, the traditional parameter estimation, as well as the suppression methods would also suffer from dynamic oscillations. To this end, this paper first investigates the oscillation propagation and typical events caused by the oscillations. Next, the oscillation model estimation method including the model-based and data-driven based methods is discussed. The benefits and difficulties of various parameter estimate techniques are highlighted. Under this context, the validity and limitations of the current power system stability are summarized. Furthermore, the different oscillation damping and mitigation measures are compared, and the major adaptability and limitations are listed for the specific application scenarios. Conclusions are drawn, and the wideband oscillation becomes the future research objective where the future work is presented at the end of the paper.