Recently, the large-scale integration of power electronic-based renewable energy power plants has changed the operation and response mechanism of the power system, resulting in several emerging oscillation issues that have seriously been threatening the system's stability. It helps us to recognize the similarities and differences among the triggering causes and formation mechanisms of oscillation scenarios. Following several typical oscillation events in the real world and the timescale decomposition method, this paper comprehensively reviews the wide-bandwidth oscillation study from the aspects of the analysis methods, possible cause, mechanism, and mitigation solution. The paper provides a perspective to classify the oscillations in the modern power systems on the basis of the oscillation frequency and the main oscillation module. This classification framework involves not only emerging oscillations in the power system with large-scale renewable energy sources integration but also includes typical oscillations in traditional power systems. It also systematically presents the relative relationship, development process, and inner influence between emerging oscillations and typical oscillations. Based on this review, the future research is suggested to focus on the relationship between different analytical methods or oscillation mechanisms, as well as the stability risk assessment of hybrid alternating current and direct current power systems.