Micro-lattice and nano-lattice structures are an exciting class of materials with better strength-to-weight and stiffness-to-weight ratios than bulk solids. Many designs and additive-manufacturing approaches (i.e., 3D printing) have emerged recently for creating such materials, with the goal of fabricating commercially available products with optimized mechanical, thermal, acoustic, and electrical properties for biomedical, aerospace, and several other applications. This Designing Materials to Revolutionize and Engineer our Future (DMREF) grant will support development of novel approaches to design a new class of disordered lattice materials that are inspired by the special transport properties, e.g., heat transfer and diffusion, of the so-called “hyperuniform” structures. Hyperuniform materials may nominally be described as materials with minimal density variation as the length scale increases. They arise naturally in biological and chemical systems and can be designed through numerical methods. Numerous studies have demonstrated that such systems facilitate efficient transport behavior with minimal attenuation while also possessing nearly optimal effective elastic stiffness and material fracture suppression. The grant will also provide effective workforce development for a diverse group of undergraduates, PhD students, and postdoctoral researchers in the multidisciplinary areas of engineering, materials science, mathematics, and physics. It will contribute to the public understanding of materials research via publications, outreach, and internship programs for high-school students and teachers. Additionally, there will be an effort to develop entrepreneurship and trainees will be supported in pursuing commercialization of their ideas.