Chromosomal rearrangements are common causes of cancer. In the majority of cases, the malignancy is induced via an altered transcription factor. The breakpoints of such translocations are often mysteriously tightly clustered in the genome. Even more surprisingly, such breakpoint clusters often contain specific genomic elements, such as topoisomerase II consensus sites, nuclear matrix attachment regions, etc. In this review, we discuss the common idea of breakpoints being induced by chromatin structure. We also touch on the question of whether the structure of corresponding proteins is related to the positions of breakpoints. Finally, we refer to recent works on chromosome territories and their distribution in the interphase nucleus.