Greer’s research focuses on creating and characterizing classes of materials with multi-scale microstructural hierarchy, which combine three-dimensional (3D) architectures with nanoscale-induced material properties. We develop fabrication and syntheses of micro- and nano-architected materials using 3D lithography, nanofabrication, and additive manufacturing (AM) techniques, and investigate – among others - their mechanical, biochemical, electrochemical, electromechanical, and thermal properties as a function of architecture, constituent materials, and microstructural detail. We strive to uncover the synergy between the internal atomic-level microstructure and the nano-sized external dimensionality, where competing material- and structure-induced size effects drive overall response and govern these properties. Specific topics include applications of 3D nano- and micro-architected materials in in chemical and biological devices, ultra lightweight energy storage systems, filters for purification and chemically-assisted separation, damage-tolerant fabrics, additive manufacturing, and smart, multi-functional materials.