In recent years, poly (ADP-ribose) polymerase (PARP) inhibition has become a promising therapeutic option for several tumors, especially for those harboring a BRCA 1–2 mutation or a deficit in the homologous recombination repair (HRR) pathway. Nevertheless, to date, PARP inhibitors are still not largely used for thoracic malignancies neither as a single agent nor in combination with other treatments. Recently, a deeper understanding of HRR mechanisms, alongside the development of new targeted and immunotherapy agents, particularly against HRR-deficient tumors, traced the path to new treatment strategies for many tumor types including lung cancer and malignant pleural mesothelioma. The aim of this review is to sum up the current knowledge about cancer-DNA damage response pathways inhibition and to update the status of recent clinical trials investigating the use of PARP inhibitors, either as monotherapy or in combination with other agents for the treatment of thoracic malignancies. We will also briefly discuss available evidence on Poly(ADP-Ribose) Glycohydrolase (PARG) inhibitors, a novel promising therapeutic option in oncology.