Damaging DNA is a current and efficient strategy to fight against cancer cell proliferation. Numerous mechanisms exist to counteract DNA damage, collectively referred to as the DNA damage response (DDR) and which are commonly dysregulated in cancer cells. Precise knowledge of these mechanisms is necessary to optimise chemotherapeutic DNA targeting. New research on DDR has uncovered a series of promising therapeutic targets, proteins and nucleic acids, with application notably via an approach referred to as combination therapy or combinatorial synthetic lethality. In this review, we summarise the cornerstone discoveries which gave way to the DNA being considered as an anticancer target, and the manipulation of DDR pathways as a valuable anticancer strategy. We describe in detail the DDR signalling and repair pathways activated in response to DNA damage. We then summarise the current understanding of non-B DNA folds, such as G-quadruplexes and DNA junctions, when they are formed and why they can offer a more specific therapeutic target compared to that of canonical B-DNA. Finally, we merge these subjects to depict the new and highly promising chemotherapeutic strategy which combines enhanced-specificity DNA damaging and DDR targeting agents. This review thus highlights how chemical biology has given rise to significant scientific advances thanks to resolutely multidisciplinary research efforts combining molecular and cell biology, chemistry and biophysics. We aim to provide the non-specialist reader a gateway into this exciting field and the specialist reader with a new perspective on the latest results achieved and strategies devised.