This dissertation work investigates the effects of earthquake rupture complexity and heterogeneities in Earth structure on near-field ground-motions. More specifically, we address two key issues in seismology: (1) near-field ground-shaking variability as function of distance and azimuth for unilateral directive ruptures, and (2) impact of rupture complexity and seismic scattering on Mach wave coherence associated with supershear rupture propagation. We examine earthquake ground-motion variability associated with unilateral ruptures based on ground-motion simulations of the MW 7.3 1992 Landers earthquake, eight simplified source models, and a MW 7.8 rupture simulation (ShakeOut) for the San Andreas fault. Our numerical modeling reveals that the ground-shaking variability in near-fault distances (< 20 km) is larger than that given by empirical ground motion prediction equations. In addition, the variability decreases with increasing distance from the source, exhibiting a power-law decay. The high near-field variability can be explained by strong directivity effects whose influence weaken as we move away from the fault. At the same time, the slope of the power-law decay is found to be dominantly controlled by slip heterogeneity. Furthermore, the ground-shaking variability is high in the rupture propagation direction whereas low in the directions perpendicular to it. However, the variability expressed as a function of azimuth is not only sensitive to slip heterogeneity, but also to rupture velocity. To study Mach wave coherence for supershear ruptures, we consider heterogeneities in rupture parameters (variations in slip, rise time and rupture speed) and 3D scattering media having small-scale random heterogeneities. The Mach wave coherence is reduced at near-fault distances (< 10 km) by the source heterogeneities. At the larger distances from the source, medium scattering plays the dominant role in reducing the Mach wave coherence. Combined effect of the source and medium heterogeneities on the supershear ruptures produce peak ground accelerations consistent with the estimates from empirical ground motion prediction equations. Therefore, we suggest that supershear ruptures may be more common in nature than detected.