The rapid advances of modern fabrications technologies require a thorough understanding of physical and mechanical properties of materials as influenced by their atomic composition, processing history and structure at the micro- and nanometer length scales. Carbon nanotubes, nanometer sized crystals, thin films and coatings, MEMS, smart materials and bio-inspired multifunctional materials are current examples employing technologies and processes that heavily depend on material properties at very small length scales. Today’s leading materials for a range of applications are hierarchical, having characteristics of structure at multiple length scales to satisfy a complex set of performance requirements and constraints. Composite materials and advanced alloy systems for transportation and infrastructure increasingly must rely on theoretical understanding at each of a range of length scales from the atomic scale upward to improve existing materials and to develop new materials to meet critical societal needs. Modern day efforts in mechanics of materials exploit recent advances in mechanics of materials that draws upon concurrent use of solid state physics, mathematics and information technology, continuum and discrete (statistical) mechanics and materials chemistry. Advanced materials derive their outstanding properties, durability and multifunctionality from heterogeneity of their underlying microstructure. There is a richness of outstanding problem sets at the intersection of theoretical and applied mathematics and materials mechanics. This state of affairs motivates the central goals of this workshop, namely to explore new and emerging mathematical approaches to multiscale modelling of evolving microstructures and to identify new and emerging mathematical approaches to interfaces in materials.