PARP inhibitors (PARPi) have been demonstrated to exhibit profound anti-tumour activity in individuals whose cancers have a defect in the homologous recombination DNA repair pathway. Here, we describe the current consensus as to how PARPi work and how drug resistance to these agents emerges. We discuss the need to refine the current repertoire of clinical-grade companion biomarkers to be used with PARPi, so that patient stratification can be improved, the early emergence of drug resistance can be detected and dose-limiting toxicity can be predicted. We also highlight current thoughts about how PARPi resistance might be treated.