Understanding and controlling vibrations in condensed matter is emerging as an essential necessity both at fundamental level and for the development of a broad variety of technological applications. Intelligent design of the band structure and transport properties of phonons at the nanoscale and of their interactions with electrons and photons impact the efficiency of nanoelectronic systems and thermoelectric materials, permit the exploration of quantum phenomena with micro- and nanoscale resonators, and provide new tools for spectroscopy and imaging. In this colloquium we assess the state of the art of nanophononics, describing the recent achievements and the open challenges in nanoscale heat transport, coherent phonon generation and exploitation, and in nano- and optomechanics. We also underline the links among the diverse communities involved in the study of nanoscale phonons, pointing out the common goals and opportunities.