Rapid improvement in seismic data acquisition and computational modeling capability provides an unprecedented opportunity to gain new insights into the physics of earthquakes. More detailed observations and more realistic models support that earthquakes interact with fault mechanics at a wide range of scales. In this talk, I will explore the features of both small and large earthquakes and investigate their physical processes. By studying M-1 to M4 earthquakes associated with fluid injection in oil and gas industry, we find fluid migration leaves significant signatures in the magnitude-frequency distributions of induced earthquakes. For M4 to M8 earthquakes, ruptures in damaged fault zones can potentially explain the discrepancy between observed and theoretically predicted rupture speeds. For M8+ earthquakes, the geometry of the subduction wedge affects whether earthquake rupture can reach the trench and cause unusually large slip at shallow depths. In each case, the integration of seismic observations and numerical models enables us to identify the fundamental processes, make physical predictions, and reduce the non-uniqueness of the interpretation. Understanding how earthquakes interact with fault mechanics will be an important step forward in developing physics-based tools for assessing earthquake hazard and reducing earthquake risk.