In this article, we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut—the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially varying material properties onto the microstructures with the corresponding properties to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, that is, several orders of magnitude higher than what can be achieved with current systems.