Materials exhibiting multidimensional structure with characteristic lengths ranging from the nanometer to the micrometer scale have extraordinary potential for emerging optical applications based on the regulation of light-matter interactions via the mesoscale organization of matter. As the structural dimensionality increases, the opportunities for controlling light-matter interactions become increasingly diverse and powerful. Recent advances in multidimensional structures have been demonstrated that serve as the basis for three-dimensional photonic-bandgap materials, metamaterials, optical cloaks, highly efficient low-cost solar cells, and chemical and biological sensors. In this Review, the state-of-the-art design and fabrication of multidimensional architectures for functional optical devices are covered and the next steps for this important field are described.