Magnetospheric ions, solar wind ions, and locally produced pick-up ions can impact the atmospheres of objects in the solar system, transferring energy by collisions with atmospheric atoms and molecules. This can result in an expansion of the atmospheric corona with a fraction of the energetic atoms or molecules being lost (sputtered) from the atmosphere. The expanded corona presents a larger target to the incident plasma, which in turn enhances pick-up ion formation and collisional ejection. In this manner a significant flux of atoms or molecules can be lost from an atmosphere, affecting its long-term evolution. This has been shown to be an important process for the dynamics and evolution of the atmosphere of lo, which is bombarded by the Jovian magnetospheric plasma, and for loss of atmosphere from Titan. Sputtering by pick-up ion bombardment has been shown to remove material from the atmosphere of Mars affecting the observed isotope ratios, and energetic O+ precipitation affects the Earth's thermosphere. The physics of ion bombardment of a gas which leads to atmospheric sputtering is described here. Analytic expressions derived from transport equations are shown to be useful for estimating the sputtering rate. These are compared to results from transport and Monte-Carlo calculations.