DNA is the molecule of heredity: it encodes the genetic information that is necessary for cells to survive, grow, divide and differentiate into tissues that make up organisms. When this information stored in DNA is changed, this is referred to as mutation. In humans and other animals, mutations that happen in germline cells can lead to disease phenotypes in the offspring, while mutations in somatic cells can cause tumors (or, they may potentially contribute to aging of tissues). In many cancers, and potentially in some healthy cells, a large number of mutations can accumulate because a DNA repair system has failed, which is a common risk factor for cancer. The HYPER-INSIGHT project is interested in properties of cancer cells after they accumulate a large number of mutations (“hypermutation”). This can help us understand how the human cells copy and repair DNA, with implications for cancer research. Additionally, cells undergoing hypermutation might develop a dependency on certain genes to help them cope with deficient DNA repair; we have searched for such genes, which could be exploited therapeutically, to selectively target cancer cells while sparing healthy tissues. The conclusions of the HYPER-INSIGHT project have significantly advanced our understanding of the landscape of somatic mutations in cancer. Through large-scale genomic analyses and development of novel statistical methodologies, we have generated insights into the organization of DNA replication and repair processes across chromosomes, the impact of positive and negative selection on somatic mutations and copy number alterations, and the identification of cancer vulnerabilities stemming from the mutator phenotypes of tumors. Our conclusions underscore the potential for harnessing the knowledge of mutagenesis in cancer to develop more effective and personalized therapies. The HYPER-INSIGHT project has opened new avenues for the global research efforts to reduce the burden of cancer on society and improve patient outcomes.