Ovarian cancer (OC) is the seventh most common type of cancer in women worldwide. Treatment for OC usually involves a combination of surgery and chemotherapy with carboplatin and paclitaxel. Platinum-based agents exert their cytotoxic action through development of DNA damage, including the formation of intra- and inter-strand cross-links, as well as single-nucleotide damage of guanine. Although these agents are highly efficient, intrinsic and acquired resistance during treatment are relatively common and remain a major challenge for platinum-based therapy. There is strong evidence to show that the functionality of various DNA repair pathways significantly impacts tumor response to treatment. Various DNA repair molecular components were found deregulated in ovarian cancer, including molecules involved in homologous recombination repair (HRR), nucleotide excision repair (NER), mismatch repair (MMR), non-homologous end-joining (NHEJ), and base excision repair (BER), which can be possibly exploited as novel therapeutic targets and sensitive/effective biomarkers. This review attempts to summarize published data on this subject and thus help in the design of new mechanistic studies to better understand the involvement of the DNA repair in the platinum drugs resistance, as well as to suggest new therapeutic perspectives and potential targets.