Complex rearrangements arise frequently in cancer, causing complex derivative alleles and copy number changes. Though subset of patterns can be readily classified into previously known categories (chromothripsis, chromoplexy, breakage fusion bridge cycles, templated insertion chains), the evolutionary origin and functional impact of many complex cancer structural variants remains obscure. The allelic phase of rearranged loci, specifically the distribution of rearranged junctions across linear or circular alleles, can yield insight into the mutational processes that gave rise to recurrent rearrangement patterns. Through analysis of over 3000 WGS cancer genome graphs, we have identified novel complex rearrangement event types that we call rigma (genomic “rifts” comprising clusters of low copy deletion junctions), pyrgo (genomic “towers” comprising clusters of low copy duplication junctions), and tyfonas (genomic “typhoons” representing clusters of high copy fold back inversions). To dissect the allelic structure of rearrangement patterns, we employed Bionano optical mapping and 10X Chromium linked reads on select cancer cell lines harboring WGS evidence of rigma, pyrgo, tyfonas, and chromothripsis. We corroborate select results with FISH and long-range profiles from ONT Nanopore and Hi-C assays. Unlike chromothripsis, we show that rigma comprise overlapping deletion junctions that are out of phase rather than present on a single allele. Our analyses of rigma provide evidence for a novel structural variant mutational process that progressively (rather than catastrophically) alters genomic loci at late replicating fragile sites, likely playing an important role in Esophageal carcinoma tumorigenesis. In contrast, pyrgo occur at early-replicating super-enhancers and are enriched in breast, ovarian, and endometrial tumors arising in the setting of inherited or acquired BRCA1 loss. Our results demonstrate how the analysis of variant phase can be used to classify and improve the mechanistic understanding of complex rearrangements.