In this article, we review recent advances in the understanding and analysis of damage initiation and evolution in laminate structures with brittle outerlayers and compliant sublayers in concentrated loading. The relevance of such damage to lifetime-limiting failures of engineering and biomechanical layer systems is emphasized. We describe the results of contact studies on monolayer, bilayer, trilayer, and multilayer test specimens that enable simple elucidation of fundamental damage mechanics and yet simulate essential function in a wide range of practical structures. Damage processes are observed using post mortem (“bonded-interface”) sectioning and direct in situ viewing during loading. The observations reveal a competition between damage modes in the brittle outerlayers—cone cracks or quasiplasticity at the top (near-contact) surfaces and laterally extending radial cracks at the lower surfaces. In metal or polymeric support layers, yield or viscoelasticity can become limiting factors. Analytical relations for the critical loads to initiate each damage mode are presented in terms of key system variables: geometrical (layer thickness and indenter radius); material (elastic modulus, strength and toughness of brittle components, hardness of deformable components). Such relations provide a sound physical basis for the design of brittle layer systems with optimal damage thresholds. Other elements of the damage process—damage evolution to failure, crack kinetics (and fatigue), flaw statistics, and complex (tangential) loading—are also considered.