Phonons—quanta of crystal lattice vibrations—reveal themselves in electrical, thermal, optical, and mechanical phenomena in materials. Phonons carry heat, scatter electrons, and affect light–matter interactions. Nanostructures opened opportunities for tuning the phonon spectrum and related properties of materials for specific applications, thus realizing what was termed phonon engineering. Recent progress in graphene and two-dimensional van der Waals materials has led to a better understanding of phonon physics and created additional opportunities for controlling phonon interactions and phonon transport at room temperature. This article reviews the basics of phonon confinement effects in nanostructures, describes phonon thermal transport in graphene, discusses phonon properties of van der Waals materials, and outlines practical applications of low-dimensional materials that rely on phonon properties.