As reported in the 2019 National Academies Press ‘Frontiers of Materials Research: A Decadal Survey’, topology optimization is pushing the frontiers of architected material design by decoupling and independently optimizing material properties and functionality. Topology optimization offers a mathematical framework to determine the most efficient material layout for prescribed constraints and loading conditions. It offers a framework for accessing unexplored and previously unachievable areas of material-property space. Simultaneously, with the development of Additive Manufacturing (AM) technology, there is enormous potential to design materials and structures, in two and three dimensions, with controlled architecture, topology, and new multifunctional performance. For example, design approaches may include multiple scales, multiple material phases, integration of manufacturing processes and uncertainty. This symposium will feature several invited speakers who are innovating methods and applications of design and topology optimization for materials.