A complete description of how an earthquake occurs can be achieved with a physically self-consistent modeling framework where wave propagation is combined with fracture mechanics to simulate the initiation, growth, and arrest of fault motion. To this end, dynamic rupture simulations are used to reproduce or predict dynamic and static deformations through time and space and give insight into the frequency-dependent rupture process. This dissertation assessed the rupture dynamics of large earthquakes in two separate tectonic environments using two different approaches. The major contribution of this work is the use of high-resolution geophysical data to constrain rupture dynamics and uncover controls on future seismic hazard in subduction or strike-slip fault systems. In chapter 2 I developed 2-D dynamic rupture simulations focused on the transition zone region between the locked and creeping regions of the Cascadia megathrust. I used geode- tic inversions for shear stress-rate to constrain possible dynamic stress-drop amplitudes within the locked and transition regions. While the initial conditions suggested an energetically unfavorable condition for deeper rupture, my models captured the exact opposite. Deeper rupture at speeds exceeding the shear-wave velocity (supershear) is possible given the geodetic inversion results, unless the transition region has a dynamic frictional behavior that strongly increases in response to slip. This study suggested the possibility of a wider Cascadia earthquake source model and that one possible mechanism for high-frequency energy radiation down-dip might be when the there is a supershear rupture transition. In chapter 3 I extended the 2-D simulation framework and developed the first fully dynamic 3-D rupture simulations for the Cascadia subduction zone. I developed an approach to estimate dynamic stress-drop along the Cascadia megathrust using geodetic coupling models of slip-rate deficit. I found that the relative dynamic stress-drop amplitude in the central Cascadia region exerts the greatest influence on whether or not margin-wide ruptures can develop. I also showed several non-unique simulations that can provide a close match to subsidence data from the last Cascadia megathrust event in 1700 A.D. - under- scoring the importance of offshore geodetic data to rule out competing ideas of interseismic strain accumulation offshore. Finally, chapter 4 investigated elastic stresses radiated from the 2019 Ridgecrest Sequence mainshock using 2-D dynamic rupture simulations. I focused on the dynamic stress changes experienced by the Garlock fault, a major strike-slip fault in the Eastern California Shear zone, during the coseismic rupture phase. I found that peak Coulomb stresses arrive at the Garlock < 1 minute from the mainshock nucleation. The simulations resolved key kinematic rupture parameters such as low mainshock rupture speeds (≤ 2.0 km/s) and slip amplitudes through the hypocenter.