The DNA damage response (DDR), a set of signaling pathways for DNA damage detection and repair, maintains genomic stability when cells are exposed to endogenous or exogenous DNA-damaging agents. Alterations in these pathways are strongly associated with cancer development, including ovarian cancer (OC), the most lethal gynecologic malignancy. In OC, failures in the DDR have been related not only to the onset but also to progression and chemoresistance. It is known that approximately half of the most frequent subtype, high-grade serous carcinoma (HGSC), exhibit defects in DNA double-strand break (DSB) repair by homologous recombination (HR), and current evidence indicates that probably all HGSCs harbor a defect in at least one DDR pathway. These defects are not restricted to HGSCs; mutations in ARID1A, which are present in 30% of endometrioid OCs and 50% of clear cell (CC) carcinomas, have also been found to confer deficiencies in DNA repair. Moreover, DDR alterations have been described in a variable percentage of the different OC subtypes. Here, we overview the main DNA repair pathways involved in the maintenance of genome stability and their deregulation in OC. We also recapitulate the preclinical and clinical data supporting the potential of targeting the DDR to fight the disease.