Thoracic cancers comprise non-small cell lung cancers (NSCLCs), small cell lung cancers (SCLCs) and malignant pleural mesotheliomas (MPM). Collectively, they account for the highest rate of death from malignancy worldwide. Genomic instability is a universal feature of cancer, which fuels mutations and tumour evolution. Deficiencies in DNA damage response (DDR) genes amplify genomic instability. Homologous recombination deficiency (HRD), resulting from BRCA1/BRCA2 inactivation, is exploited for therapeutic synthetic lethality with poly-ADP ribose polymerase (PARP) inhibitors in breast and ovarian cancers, as well as in prostate and pancreatic cancers. However, DDR deficiency and its therapeutic implications are less well established in thoracic cancers. Emerging evidence suggests that a subset of thoracic cancers may harbour DDR deficiency and may, thus, be effectively targeted with DDR agents. Here, we review the current evidence surrounding DDR in thoracic cancers and discuss the challenges and promise for achieving clinical benefit with such therapeutics.