Tumour-associated genetic changes frequently involve DNA translocation or deletion. Many of these events will have arisen from initial genomic damage, induced by either the activity of endogenous metabolic processes or from exposure to environmental genotoxic agents. Although initial genomic damage will have been widely distributed, tumorigenic events are confined to certain DNA target sites. Furthermore, within these target sites there appear to be regions of preferential DNA rearrangement, and examination of these sites implies that the location and extent of such rearrangement may be influenced by DNA primary and secondary structure rather than simply by the point of damage. We selectively review evidence relating to DNA structures that may predispose certain regions of the genome to damage-induced rearrangement, and discuss the possible role of interstitial, inverted telomere-like sequence arrays in promoting chromosomal events of a type known to be associated with some human and animal tumours.