Compared to the number of reports on the self-assembly of spherical nanoparticles forming superlattices, relatively fewer studies have addressed the assembly of polyhedral metal and semiconductor nanocrystals for the formation of supercrystals with well-defined geometric shapes. These polyhedral supercrystals are considered as a new class of superlattice structures in which particle morphology strongly dictates the shapes of resulting supercrystals if the particles are larger than 20 nm. This review provides examples and advances in fabricating supercrystals on a substrate during the process of solvent evaporation and through diffusion transport of surfactant to generate free-standing supercrystals. The diversity of supercrystal morphologies observed is illustrated. In many cases, the supercrystal formation process has been found to be surfactant-mediated with surfactant molecules residing between adjacent nanocrystals. Polyhedral nanocrystal assembly was found to be strongly shape-guided. Thus, the formation of polyhedral supercrystals offers a unique opportunity to reconsider the forces involved from a more global perspective instead of focusing on mainly local interactions. Efforts have been made to record the entire supercrystal formation process. Finally, some results of properties of supercrystals and future directions for supercrystal research are provided. (C) 2015 Elsevier Ltd. All rights reserved.