This book covers multi-scale damage modeling of composite materials while expanding classical techniques to consider advanced fiber architectures such as woven textile composites. Classical methods are expanded to the analysis of thick-section composites which opens the regime to ballistic and low velocity impact applications. These analyses are inherently multi-scale in nature, as deformation and failure mechanisms involve multiple phenomena on several length scales. Nano and micro scale modeling utilizing molecular and dynamic (MD) and advanced fracture computational techniques (XFEM and cohesive element approaches) can be employed to determine the property enhancements and toughening effects of nanoparticulate and carbon nanotube reinforcements. Material-by-design approaches to composite material development will be achieved through modeling of representative microstructures at multiple length scales.