Structural variants can contribute to oncogenesis through a variety of mechanisms, yet, despite their importance, the identification of structural variants in cancer genomes remains challenging. Here, we present an integrative framework for comprehensively identifying structural variation in cancer genomes. For the first time, we apply next-generation optical mapping, high-throughput chromosome conformation capture (Hi-C) techniques, and whole genome sequencing to systematically detect SVs in a variety of cancer cells. Using this approach, we identify and characterize structural variants in up to 29 commonly used normal and cancer cell lines. We find that each method has unique strengths in identifying different classes of structural variants and at different scales, suggesting that integrative approaches are likely the only way to comprehensively identify structural variants in the genome. Studying the impact of the structural variants in cancer cell lines, we identify widespread structural variation events affecting replication timing and the functions of non-coding sequences in the genome, including the deletion of distal regulatory sequences, alteration of DNA replication timing, and the creation of novel 3D chromatin structural domains. These results underscore the importance of comprehensive structural variant identification and indicate that non-coding structural variation may be an underappreciated mutational process in cancer genomes.