Acoustic nanocavities display localized acoustic states similar to the confined electronic levels in atoms and quantum wells. Exploiting this parallel and concepts used in photonics, we describe novel acoustic devices operative in the THz range (nm wavelength) based on cavities as the basic building block. These include phonon molecules, acoustic minibands, structures displaying acoustic Wannier-Stark ladders and Bloch oscillations, and devices with generalized engineered phonon potentials and confined energy states. We demonstrate that both the spectra and the dynamics of acoustic waves can be tailored with great versatility in these devices.