Cavity (void) formation and swelling in non-fissile materials during neutron irradiation and charged particle bombardments are reviewed. Helium is the most important inert gas and is primarily active as a cavity nucleant. It also enhances formation of dislocation structure. Preimplantation of helium overstimulates cavity nucleation and gives a different temperature response of swelling than when helium is coimplanted during the damage process. Helium affects, and is affected by, radiation-induced phase instability. Many of these effects are explainable in terms of cavity nucleation on submicroscopic critical size gas bubbles, and on the influence of the neutral sink strength of such bubbles. Titanium and zirconium resist cavity formation when vacancy loops are present.