Earth's topographic surface forms an interface across which the geodynamic and geomorphic engines interact. This interaction is best observed along crustal margins where topography is created by active faulting and sculpted by geomorphic processes. Crustal deformation manifests as earthquakes at centennial to millennial timescales. Given that nearly half of Earth's human population lives along active fault zones, a quantitative understanding of the mechanics of earthquakes and faulting is necessary to build accurate earthquake forecasts. My research relies on the quantitative documentation of the geomorphic expression of large earthquakes and the physical processes that control their spatiotemporal distributions. The first part of my research uses high-resolution topographic lidar data to quantitatively document the geomorphic expression of historic and prehistoric large earthquakes. Lidar data allow for enhanced visualization and reconstruction of structures and stratigraphy exposed by paleoseismic trenches. Lidar surveys of fault scarps formed by the 1992 Landers earthquake document the centimeter-scale erosional landforms developed by repeated winter storm-driven erosion. The second part of my research employs a quasi-static numerical earthquake simulator to explore the effects of fault roughness, friction, and structural complexities on earthquake-generated deformation. My experiments show that fault roughness plays a critical role in determining fault-to-fault rupture jumping probabilities. These results corroborate the accepted 3-5 km rupture jumping distance for smooth faults. However, my simulations show that the rupture jumping threshold distance is highly variable for rough faults due to heterogeneous elastic strain energies. Furthermore, fault roughness controls spatiotemporal variations in slip rates such that rough faults exhibit lower slip rates relative to their smooth counterparts. The central implication of these results lies in guiding the interpretation of paleoseismically derived slip rates that are used to form earthquake forecasts. The final part of my research evaluates a set of Earth science-themed lesson plans that I designed for elementary-level learning-disabled students. My findings show that a combination of concept delivery techniques is most effective for learning-disabled students and should incorporate interactive slide presentations, tactile manipulatives, teacher-assisted concept sketches, and student-led teaching to help learning-disabled students grasp Earth science concepts.