Organizing the DNA to fit inside a spatially constrained nucleus is a challenging problem that has attracted the attention of scientists across all disciplines of science. Increasing evidence has demonstrated the importance of genome geometry in several cellular contexts that affect human health. Among several approaches, the application of sequencing technologies has substantially increased our understanding of this intricate organization, also known as chromatin interactions. These structures are involved in transcriptional control of gene expression by connecting distal regulatory elements with their target genes and regulating co-transcriptional splicing. In addition, chromatin interactions play pivotal roles in the organization of the genome, the formation of structural variants, recombination, DNA replication and cell division. Mutations in factors that regulate chromatin interactions lead to the development of pathological conditions, for example, cancer. In this review, we discuss key findings that have shed light on the importance of these structures in the context of cancers, and highlight the applicability of chromatin interactions as potential biomarkers in molecular medicine as well as therapeutic implications of chromatin interactions.