Reducing mass without sacrificing mechanical integrity and performance is a critical goal in a vast range of applications. Introducing a controlled amount of porosity in a strong and dense material (hence fabricating a cellular solid) is an obvious avenue to weight reduction. The mechanical effectiveness of this strategy, though, depends strongly on the architecture of the resulting cellular material (i.e., the topology of the introduced porosity). Recent progress in additive manufacturing enables fabrication of macro-scale cellular materials (both single-phase and hybrid) with unprecedented dimensional control on the unit-cell and sub-unit-cell features, potentially producing architectures with structural hierarchy from the nano to the macro-scale. As mechanical properties of materials often exhibit beneficial size effects at the nano-scale (e.g., strengthening of metals and toughening of ceramics), these novel manufacturing approaches provide a unique opportunity to translate these beneficial effects to the macro-scale, further improving the mechanical performance of architected materials. The enormous design space for architected materials, and the strong relationship between the topological features of the architecture and the effective physical and mechanical properties of the material at the macro-scale, present both a huge opportunity and an urgent need for the development of suitable optimal design strategies. Here we present a number of strategies for the advanced manufacturing, characterization and optimal design of a variety of lightweight architected materials with unique combinations of mechanical properties (stiffness, strength, damping coefficient…). The urgent need to form strong synergies among the fields of additive manufacturing, topology optimization and architectureproperties relations is emphasized throughout.