Developing novel targeted anticancer therapies is a major goal of current research. The use of poly(ADP-ribose) polymerase (PARP) inhibitors in patients with homologous recombination-deficient tumours provides one of the best examples of a targeted therapy that has been successfully translated into the clinic. The success of this approach has so far led to the approval of four different PARP inhibitors for the treatment of several types of cancers and a total of seven different compounds are currently under clinical investigation for various indications. Clinical trials have demonstrated promising response rates among patients receiving PARP inhibitors, although the majority will inevitably develop resistance. Preclinical and clinical data have revealed multiple mechanisms of resistance and current efforts are focused on developing strategies to address this challenge. In this Review, we summarize the diverse processes underlying resistance to PARP inhibitors and discuss the potential strategies that might overcome these mechanisms such as combinations with chemotherapies, targeting the acquired vulnerabilities associated with resistance to PARP inhibitors or suppressing genomic instability.