The paper briefly describes the main features of the damage produced by swift heavy ion (SHI) irradiation. After a short revision of the widely used thermal spike concept, it focuses on cumulative mechanisms of track formation which are alternative to those based on lattice melting (thermal spike models). These cumulative mechanisms rely on the production of point defects around the ion trajectory, and their accumulation up to a final lattice collapse or amorphization. As to the formation of point defects, the paper considers those mechanisms relying on direct local conversion of the excitation energy into atomic displacements (exciton models). A particular attention is given to processes based on the non-radiative recombination of excitons that have become self-trapped as a consequence of a strong electron-phonon interaction (STEs). These mechanisms, although operative under purely ionizing radiation in some dielectric materials, have been rarely invoked, so far, to discuss SHI damage. They are discussed in this paper together with relevant examples to materials such as Cu 3 N, alkali halides, SiO 2 , and LiNbO 3 .