Significance: It has been a long-standing effort to create materials with low density but high strength. Technical foams are very light, but compared with bulk materials, their strength is quite low because of their random structure. Natural lightweight materials, such as bone, are cellular solids with optimized architecture. They are structured hierarchically and actually consist of nanometer-size building blocks, providing a benefit from mechanical size effects. In this paper, we demonstrate that materials with a designed microarchitecture, which provides both structural advantages and size-dependent strengthening effects, may be fabricated. Using 3D laser lithography, we produced micro-truss and -shell structures from ceramic–polymer composites that exceed the strength-to-weight ratio of all engineering materials, with a density below 1,000 kg/m ³ .