Colloidal nanocrystals are successfully used as nanoscale building blocks for creating hierarchical solids with structures that range from amorphous networks to sophisticated periodic superlattices. Recently, it has been observed that these superlattices exhibit collective vibrations, which stem from the correlated motion of the nanocrystals, with their surface-bound ligands acting as molecular linkers. In this Perspective, we describe the work so far on collective vibrations in nanocrystal solids and their as-of-yet untapped potential for phononic applications. With the ability to engineer vibrations in the hypersonic regime through the choice of nanocrystal and linker composition, as well as by controlling their size, shape and chemical interactions, such superstructures offer new opportunities for phononic crystals, acoustic metamaterials and optomechanical systems.