Nanocrystals of semiconductors, oxides, and metals comprise a distinct class of artificial materials because their electronic, magnetic, and optical properties are strongly controlled by their size and shape. Nanocrystals can be also used as elemental building blocks to create “nanocrystal solids” having long-range crystalline order on a scale that would otherwise require lithography. Compound nanocrystal solids can also be created, such as binary nanocrystal solids, in which two types of nanocrystals differing in size and material composition form an ordered solid. The aim of the research is to elucidate and develop rational design principles, using a combination of density-functional theory and semi-empirical methods, that will ultimately enable experimentalists to create new nanocrystal solids with useful properties.