Cancer genomes frequently harbor structural chromosomal rearrangements that disrupt the linear DNA sequence order and copy number. To date, diverse classes of structural variants have been identified across multiple cancer types. These aberrations span a wide spectrum of complexity, ranging from simple translocations to intricate patterns of rearrangements involving multiple chromosomes. Although most somatic rearrangements are acquired gradually throughout tumorigenesis, recent interrogation of cancer genomes have uncovered novel categories of complex rearrangements that arises rapidly through a one-off catastrophic event, including chromothripsis and chromoplexy. Here we review the cellular and molecular mechanisms contributing to the formation of diverse structural rearrangement classes during cancer development. Genotoxic stress from a myriad of extrinsic and intrinsic sources can trigger DNA double-strand breaks that are subjected to DNA repair with potentially mutagenic outcomes. We also highlight how aberrant nuclear structures generated through mitotic cell division errors, such as rupture-prone micronuclei and chromosome bridges, can instigate massive DNA damage and the formation of complex rearrangements in cancer genomes.