In the past decade, we have seen the emergence of sequence-based methods to understand chromosome organization. With the confluence of in situ approaches to capture information on looping, topological domains, and larger chromatin compartments, understanding chromatin-driven disease is becoming feasible. Excitingly, recent advances in single molecule imaging with capacity to reconstruct “bulk-cell” features of chromosome conformation have revealed cell-to-cell chromatin structural variation. The fundamental question motivating our analysis of the literature is, can altered chromatin structure drive tumorigenesis? As our community learns more about rare disease, including low mutational frequency cancers, understanding “chromatin-driven” pathology will illuminate the regulatory structures of the genome. We describe recent insights into altered genome architecture in human cancer, highlighting multiple pathways toward disruptions of chromatin structure, including structural variation, noncoding mutations, metabolism, and de novo mutations to architectural regulators themselves. Our analysis of the literature reveals that deregulation of genome structure is characteristic in distinct classes of chromatin-driven tumors. As we begin to integrate the findings from single cell imaging studies and chromatin structural sequencing, we will be able to understand the diversity of cells within a common diagnosis, and begin to define structure–function relationships of the misfolded genome.