When considering nuclei as finite-size, droplet-like collections of protons and neutrons, several normal modes of nuclear-density vibration can be conceived. The most prominent modes are the oscillation of neutron matter against proton matter, associated with the giant dipole resonance, and the compressional modes. The restoring force of these oscillations originates largely in bulk properties of nuclear matter, namely the symmetry energy and incompressibility. Surface modes, on the other hand, are governed by the properties of the diffuse nuclear surface and the nuclear shell structure. They are excited at lower energies (up to a few MeV) and affect the outcome of important nuclear reactions. We will discuss one special surface mode, of dipole form, which has been observed in several light and medium to heavy nuclei. It is key to a definitive understanding of the so-called pygmy dipole strength, and its properties can be used to quantify isospin mixing and to improve a variety of nuclear models aiming at a realistic description of exotic nuclei and processes of astrophysical interest.