Earthquake fault zones exhibit hierarchical damage and granular structures with evolving geometrical and material properties. Understanding how repeated brittle deformation form the structures and how the structures affect subsequent earthquakes is a rich problem involving coupling of various processes that operate over broad space and time scales. The diverse state-of-the-art papers collected here show how insight can come from many fields including statistical physics, structural geology and rock mechanics at large scales; elasticity, friction and nonlinear continuum mechanics at intermediate scales; and fracture mechanics, granular mechanics and surface physics at small scales. This volume will be useful to students and professional researchers from Earth Sciences, Material Sciences, Engineering, Physics and other disciplines, who are interested in the properties of natural fault zones and the processes that occur between and during earthquakes.