Cells have evolved a DNA damage response (DDR) pathway to monitor the integrity of their genome, which is tightly associated with cell cycle checkpoint controls, arresting cells to allow for DNA repair before continuing through the cell cycle. Defects in the DDR and checkpoint mechanisms frequently occur in human cancers, with failure of the cell to repair the DNA damage leading to genomic instability, increased mutation load, and cellular transformation. The loss of a DNA damage checkpoint in a tumour should make it vulnerable to checkpoint override strategies, providing therapeutic opportunities to inhibit mechanisms that compensate for the defect. Here we review the DDR pathway and cell cycle checkpoint responses to DNA damage, and explain how defects in these mechanisms present a significant opportunity for therapeutic intervention. These defects can be exploited using a synthetic lethal approach to target tumours with these defects and having limited normal tissue toxicity.