Ultrafast excitation of nanoparticles can excite the acoustic vibrational modes of the structure that correlate with the expansion coordinates. These modes are frequently seen in transient absorption experiments on metal nanoparticle samples and occasionally for semiconductors. The aim of this review is to give an overview of the physical chemistry of nanostructure acoustic vibrations. The issues discussed include the excitation mechanism, how to calculate the mode frequencies using continuum mechanics, and the factors that control vibrational damping. Recent results that demonstrate that the high frequencies inherent to the acoustic modes of nanomaterials trigger a viscoelastic response in surrounding liquids are also discussed, as well as vibrational coupling between nanostructures and mode hybridization within the nanostructures. Mode hybridization provides a way of manipulating the lifetimes of the acoustic modes, which is potentially useful for applications such as mass sensing.