Introduction: Damage and failure of heterogeneous media: basic features and common characteristics.-Framework of statistical meso-mechanics: why and how statistical meso-mechanics is.- Mathematical essentials in statistical meso-mechanics.- Part A Quasi-statically Statistical Evolution of Deformation and Damage in Media with Mesoscopic Heterogeneities: Coupled average (CA).- Elastic and statistically-brittle (ESB) constitutive model, Global mean field (GMF) approximation.- Continuous bifurcation and localization of deformation, Regional mean field (RMF) approximation.- Size effect.- Experimental issues related to statistical meso-mechanics.- Numerical issues related to heterogeneous meso-elements.- Application to failure wave (one-dimensional strain state).- Application to metal foams.- Application to concrete under bi-axial compression.- Part B Time-Dependent Processes of Micro-damage Population: Background and methodology.- Fundamental equation of microdamage evolution.- General solution to evolution of microdamage number density.- Closed formulation of continuum damage based on microdamage evolution.- Deborah number and its significance in the evolution of microdamage.- Spallation - tensile failure resulting from microcracks under stress waves.- Short fatigue cracks.- More cases of time-dependent processes related to microdamage.- Brief summary of Part B.- Part C Critical Catastrophe: Evolution induced catastrophe (EIC).- Energy transfer and catastrophe considering damage localization.- Sample specificity and Trans-scale Sensitivity.- Critical Sensitivity and power-law singularity of catastrophe.- Great earthquake: the catastrophic rupture in Earth's Crust.- Perspective.