Resistance to chemo- and radiotherapy is a common event among cancer patients and a reason why new cancer therapies and therapeutic strategies need to be in continuous investigation and development. DNA damage response (DDR) comprises several pathways that eliminate DNA damage to maintain genomic stability and integrity, but different types of cancers are associated with DDR machinery defects. Many improvements have been made in recent years, providing several drugs and therapeutic strategies for cancer patients, including those targeting the DDR pathways. Currently, poly (ADP-ribose) polymerase inhibitors (PARP inhibitors) are the DDR inhibitors (DDRi) approved for several cancers, including breast, ovarian, pancreatic, and prostate cancer. However, PARPi resistance is a growing issue in clinical settings that increases disease relapse and aggravate patients’ prognosis. Additionally, resistance to other DDRi is also being found and investigated. The resistance mechanisms to DDRi include reversion mutations, epigenetic modification, stabilization of the replication fork, and increased drug efflux. This review highlights the DDR pathways in cancer therapy, its role in the resistance to conventional treatments, and its exploitation for anticancer treatment. Biomarkers of treatment response, combination strategies with other anticancer agents, resistance mechanisms, and liabilities of treatment with DDR inhibitors are also discussed.