We review the rationale for seeking inhibitors of homologous recombination (HR) repair for use in cancer therapy. Cells use HR as one way to repair DNA double-strand breaks that arise directly from treatments such as radiotherapy, or indirectly during replication when forks encounter other damage. HR occurs during the S and G₂ phases of the cell cycle and is therefore more significant in dividing cancer cells than in non-dividing cells of healthy tissue, giving a potential therapeutic advantage to inhibiting the process. Also, some tumors consist of cells that are defective in other DNA repair pathways, and such cells may be sensitive to HR repair inhibitors because of synthetic lethality, in which blocking two alternative pathways that a cell can use to reach a needed end-point has a much bigger impact than blocking either pathway alone. We review strategies for identifying HR inhibitors and discuss current progress.