An understanding of how dots couple in quantum dot molecules and arrays is needed so that the possibilities for tailored nanooptics in these systems can be explored. The properties of tunnel-coupled dots will be determined by how the dots couple through atomic-scale junctions. We present an atomistic empirical tight-binding theory of coupled, CdS nanocrystal artificial-molecules, vertically and laterally coupled InAs/GaAs self-assembled dots, and arrays of InAs/GaAs self-assembled dots. Electron states follow the artificial molecule analogy. The coupling of hole states is much more complex. There are significant departures from the artificial molecule analogy because the interdot hole coupling is determined by the hole envelope functions, as for the electron states, and by the hole atomic state near interdot interfaces.