DNA repair is a complicated process that occurs due to a network of different pathways and mechanisms for correction of DNA damages during the normal DNA biosynthesis and under the influence of external and internal factors. The study of these mechanisms and their regulation is closely related to both diagnostics and the search for ways of treating various diseases, including oncological ones. Malignant neoplasms are one of the three most widespread diseases in the world, which unfortunately often become the reason for a lethal outcome. Traditional cancer therapy aims to the DNA damage in malignant cells, and its result depends on the efficiency of the repair systems. In many cancer cells, the individual DNA repair enzymes are overexpressed, which promotes the resistance of these tumors to the therapy. On the other hand, defects in the DNA repair systems in cancer cells allow researchers to find both appropriate biomarkers for diagnostics and targets for the development of the specific and effective therapy. Currently, DNA repair inhibitors are being actively developed in order to increase the sensitivity of the tumor cells to traditional chemotherapy. The principle of synthetic lethality is used to create cell-specific drugs and to improve the effectiveness of the treatment. In this review, we discuss the current state of research and prospects for the development of inhibitors for five important DNA repair enzymes.