Nanostructures of III-V (III: Ga, In; V: N, P, As) and II-VI (II: Zn, Cd; VI: S, Se, Te) semiconductor materials have attracted a great deal of interest due to their fascinating properties, which usually differ from their bulk counterparts. There are two main reasons responsibles for such a deviation. On the one hand, the confinement of electrons (and holes) in nanostructures gives rise to a size- and shape- dependent structure of electronic levels. On the one hand, the number of atoms forming the surface of a nanostructure is a significant fraction of the total. The unsaturated surface atoms tend to reorganize in order to minimize the surface energy, favouring certain crystalline phases and eventually leading to fancy atomic arrangements. Again, the stability of each polymorph depends on the size and the morphology of the nanostructure.