Faults that accommodate earthquakes are often embedded in hundreds-meter-thick fractured rocks, i.e., fault damage zones. The San Andreas fault, for example, is surrounded by a 150-200 m wide fault damage zone with 30-40% seismic wave reductions. Because such major faults can host M7 earthquakes that cause strong ground shaking in nearby populated regions, it is essential to understand how earthquakes grow in fault damage zones and whether their source properties and ground motions are strongly modulated by the fractured rocks. My talk will demonstrate how seismic waves in damage zones can profoundly affect how fast earthquakes grow and how quickly slip arrests on the fault in dynamic rupture simulations. I will also discuss the theoretical prediction that earthquakes in damage zones can rupture faster than the shear wave speeds of host rocks. Such supershear rupture can propagate stably at a range of speeds usually considered as unstable and cause large ground motions at long distances.