Seafloor instability and secondary submarine geohazards are widely present in the ocean, posing a threat to submarine infrastructures such as coastal port facilities, offshore drilling platforms, and submarine pipelines and fiber-optic cables. However, formation mechanisms and controlling factors of seafloor instability are still poorly understood. To improve the understanding, based on the history and development of seafloor instability, this study sorts out the common categories, global distribution, and geophysical characteristics, analyzes the formation mechanisms, controlling factors, and engineering geohazards risks, and summarizes popular quantitative analysis methods for seafloor instability. Subsequently, the application and limitations of experimental simulation technology for the slope instability process are discussed. Focused on the disaster mechanism, intelligent analysis of multi-source data, and three-dimensional monitoring of seabed instability, this study proposed the development direction and countermeasures of future seafloor instability research, aiming to provide guiding suggestions for the simulation, prediction, and warning of seafloor instability.