DNA inevitably undergoes a high number of damages throughout the cell cycle. To preserve the integrity of the genome, cells have developed a complex enzymatic machinery aimed at sensing and repairing DNA lesions, pausing the cell cycle to provide more time to repair, or induce apoptosis if damages are too severe. This so-called DNA-damage response (DDR) is yet considered as a major source of resistance to DNA-damaging treatments in oncology. Recently, it has been hypothesized that cancer stem cells (CSC), a sub-population of cancer cells particularly resistant and with tumour-initiating ability, allow tumour re-growth and cancer relapse. Therefore, DDR appears as a relevant target to sensitize cancer cells and cancer stem cells to classical radio- and chemotherapies as well as to overcome resistances. Moreover, the concept of synthetic lethality could be particularly efficiently exploited in DDR. Five kinases play pivotal roles in the DDR: ATM, ATR, CHK1, CHK2 and WEE1. Herein, we review the drugs targeting these proteins and the inhibitors used in the specific case of CSC. We also suggest molecules that may be of interest for preclinical and clinical researchers studying checkpoint inhibition to sensitize cancer and cancer stem cells to DNA-damaging treatments.