This book reviews the mathematical modeling and experimental study of systems involving two or more different length scales. The effects of phenomena occurring at the lower length scales on the behavior at higher scales are of intrinsic scientific interest, but can also be very effectively used to determine the behavior at higher length scales or at the macro-level. Efforts to exploit this micro- and macro-coupling are, naturally, being pursued with regard to every aspect of mechanical phenomena. This book focuses on the changes imposed on the dynamics, strength of materials and durability of mechanical systems by related multiscale phenomena. In particular, it addresses:1: the impacts of effective dissipation due to kinetic energy trapped at lower scales2: wave propagation in generalized continua3: nonlinear phenomena in metamaterials4: the formalization of more general models to describe the exotic behavior of meta-materials5: the design and study of microstructures aimed at increasing the toughness and durability of novel materials