Subsynchronous oscillation (SSO) is classified as subsynchronous resonance, torsional interaction, or control interaction, depending on which devices or controllers are involved. Researchers have conducted numerous studies and developed methodologies on how to analyze SSO cases in different types of power systems. For these diverse mechanisms, complicated systems, and analytical methods, the overall summary and categorization of the SSO phenomena have been crucial, and numerous reviews have been published to this end. However, with the emerging inverter-based and power-electronics-based devices, in addition to the high computational capability, more advanced analytical methods have recently been researched, and more general, up-to-date literature surveys are thus needed. This study reviews the various SSO types depending on the interaction mechanisms, before investigating a number of representative SSO events in terms of the devices. Following this, the study evaluates the existing cutting-edge methods for SSO analysis and compares them to ascertain the appropriate method for specific SSO types. The review provides distinct practical considerations for the analysis to simplify the entire procedure. Ultimately, this paper presents a summary of modern SSO-damping and mitigation methods for pragmatic insight and future perspectives for a reader when dealing with old and the latest power systems.