Research on fault interaction and earthquake triggering, which is a hot issue in the field of source physics, can facilitate understanding of the underlying mechanisms of strong earthquakes and also has good application prospects in earthquake risk analysis and prediction research. Previous review articles provided detailed explanations from the perspectives of basic principles, methods, and applicability, as well as multiple earthquake case studies of stress triggering. However, the introduction to earthquake triggering from the perspective of seismicity analysis is not exhaustive, and the combination and complementarity of these two perspectives are not provided in detail. This paper summarizes the achievements and progress of research on fault interaction and earthquake triggering mechanism through the past few decades from the perspectives of physical and statistical models. The current challenges and possible future directions are reviewed and evaluated. From the perspective of the physical model, three important mechanisms of sources of fault interaction are analyzed: static stress triggering, dynamic stress triggering, and viscoelastic stress triggering, as well as the basic principles and methods of calculation. In the aspect of the statistical model, the basic principles and methods of seismicity analysis are introduced, and applications of the epidemic-type aftershock sequence (ETAS) model and b
-value in fault interaction and earthquake triggering mechanism are analyzed. From the perspective of the combination of these two models, the unified connotation of mutual verification and the basic principle of the rate-and-state friction law are introduced. The analysis points out that the stress interaction between multiple faults or earthquakes can be comprehensively studied through the two different schools of Coulomb stress calculation and the ETAS model and that cross-validation can increase the reliability of the results. Retroactive application of rate-and-state friction law can provide a new perspective for understanding the earthquake triggering relationship and fault interaction.