It is well known that most large-size earthquakes with shallow hypocentersHypocenter occur as dynamic reactivation of existing faults. However, these recurring earthquakes do not necessarily rupture the same part of the existing fault in the same way; the rupture pattern and the fault geometry may change with each earthquake. In other words, the geometry of existing faults may influence the rupture patterns of future earthquakes that will occur there, and the occurrence of these earthquakes may alter the geometry and other characteristics of existing faults. Therefore, understanding the geometry of faults will provide some key to understanding earthquake rupture phenomena. This chapter will explore, from a theoretical but fundamental perspective, how earthquake rupture contributes to the formation of non-planar faultNon-planar fault (crack) geometries and how fault geometry and earthquake rupture dynamics are interrelated.