The studies focus on detailed tests of the hypothesis that earthquake ruptures on a fault between rocks of different elastic properties propagate preferentially in the direction of slip of the more compliant side of the fault. Recent analytical and numerical studies of dynamic rupture along an interface between dissimilar materials predict that one direction of rupture will be favored over the other. This is supported by recent laboratory observations and some seismic data. If unidirectional rupture is a persistent behavior for natural fault structures with material contrasts, repeated unidirectional ruptures should leave a distinct asymmetric imprint on the microstructure of the fault zone. Preliminary observations at several exposures along the San Jacinto, San Andreas and Punchbowl faults in southern California reveal several signatures of asymmetry in both the gouge and damage zones that support this model and warrant further work. The continuing investigations map systematically the fabric and structure of fault zone gouge and damage at several sites along a number of large strike-slip faults, with the specific purpose of developing criteria to resolve rupture propagation direction. The observational work is accompanied by a theoretical parameter-space study of rupture that can migrate between and propagate simultaneously along several interfaces and theoretical simulations of rupture that can produce off-fault damage. The studies can have profound implications for many aspects of earthquake geology and physics of rupture propagation on large faults, including effective constitutive laws, suppression of branching, fault-interaction, triggering, the heat flow paradox, short rise-time of earthquake slip, and estimates of seismic shaking hazard associated with rupture of large faults.