Structural variants (SVs) can contribute to oncogenesis through a variety of mechanisms. Despite their importance, the identification of SVs in cancer genomes remains challenging. Here, we present a framework that integrates optical mapping, high-throughput chromosome conformation capture (Hi-C), and whole-genome sequencing to systematically detect SVs in a variety of normal or cancer samples and cell lines. We identify the unique strengths of each method and demonstrate that only integrative approaches can comprehensively identify SVs in the genome. By combining Hi-C and optical mapping, we resolve complex SVs and phase multiple SV events to a single haplotype. Furthermore, we observe widespread structural variation events affecting the functions of noncoding sequences, including the deletion of distal regulatory sequences, alteration of DNA replication timing, and the creation of novel three-dimensional chromatin structural domains. Our results indicate that noncoding SVs may be underappreciated mutational drivers in cancer genomes.