3D genome organization regulates gene expression in different physiological and pathological contexts. Characterization of chromatin structure at different scales has provided information about how the genome organizes in the nuclear space, from chromosome territories, compartments of euchromatin and heterochromatin, topologically associated domains to punctual chromatin loops between genomic regulatory elements and gene promoters. In recent years, chromosome conformation capture technologies have also been used to characterize structural variations (SVs) de novo in pathological conditions. The study of SVs in cancer, has brought information about transcriptional misregulation that relates directly to the incidence and prognosis of the disease. For example, gene fusions have been discovered arising from chromosomal translocations that upregulate oncogenes expression, and other types of SVs have been described that alter large genomic regions encompassing many genes. However, studying SVs in 2D cannot capture all their regulatory implications in the genome. Recently, several bioinformatic tools have been developed to identify and classify SVs from chromosome conformation capture data and clarify how they impact chromatin structure in 3D, resulting in transcriptional misregulation. Here, we review recent literature concerning bioinformatic tools to characterize SVs from chromosome conformation capture technologies and exemplify their vast potential to rebuild the 3D landscape of genomes in cancer. The study of SVs from the 3D perspective can produce essential information about drivers, molecular targets, and disease evolution.