Rocks generally have a complex microstructure and contain discontinuities and heterogeneities at several scales that make their behavior more complex than most usual engineering materials. Issues related to failure and strength and their relations to the modes of deformation and degradation must be addressed as a multi-physics and multi-scale problem involving several different spatial and temporal scales. The objective of the chapter is to present a review of recent research on understanding and modelling of failure mechanisms including the effect of pore pressure, temperature, chemical reactions and microstructure in relation to strain localization and stability analysis. The geophysical implications of these instabilities in underground reservoirs and in seismic faults are discussed.