Waves in solar and stellar atmospheres have been proposed more than fifty years ago to heat the chromosphere and the corona. Their usefulness as a means to explain an important phenomenon gave wave science its initial impetus. However, since then, waves and oscillations have become a great astrophysical topic of their own. In an inhomogeneous medium, waves occur in immense variety. The theory of waves explores this complexity and highlights modes and properties that are important in stellar atmospheres. We have seen steady progress in this fundamental endeavour that has recently been accelerated through the use of numerical simulations. The discovery, three decades ago, of waves in the solar and stellar interiors and later in the corona, although at low energy levels, opened a new field: the diagnostic use of waves. Seismology of the interior has become a booming field of solar and stellar physics, and observed oscillations have been used to derive the magnetic field strength and to explore the corona.