This book summarizes the results of a research programme financed by the "Deutsche Forschungsgemeinschaft" in the field of deformation and failure in granular and porous media. It presents the recent engineering as well as mathematical key aspects of this field for a broad community. Its main focus is on the dynamics response under large and catastrophic deformations, covering the fundamentals and dynamical processes of porous and granular materials as well as their related sub-scale and micro-mechanical effects.Special emphasis is placed on the modeling and theory of avalanches, debris and mud flows.