Material properties are governed by the chemical composition and spatial arrangement of constituent elements at multiple length-scales.  This fundamentally limits material properties with respect to each other creating trade-offs when selecting materials for specific applications.  For example, strength and density are inherently linked so that, in general, the more dense the material, the stronger it is in bulk form.  We are combining advanced microstructural design, using flexure and screw theory as well as topology optimization, with advanced additive micro- and nanomanufacturing techniques to create new material systems with previously unachievable property combinations – mechanical metamaterials.  The performance of these materials is fundamentally controlled by geometry at multiple length-scales rather than chemical composition alone.  We have demonstrated designer properties of these mechanical metamaterials in polymers, metals, ceramics and combinations thereof. Properties include ultra-stiff lightweight materials, negative stiffness, and negative thermal expansion. Our additive micro-manufacturing techniques include Projection Microstereolithography (PMSL), Direct Ink Writing (DIW), and Electrophoretic Deposition (EPD) as well as some new advanced concepts such as holographic lithography. These tools are capable of generating the designed structures which are highly three-dimensional micro- and nano-scale architectures with multiple constituent materials in the same structure.