The poly(ADP-ribose) polymerase (PARP) protein superfamily has wide-ranging roles in cellular processes such as DNA repair and WNT signalling. Efforts to pharmacologically target PARP enzymes have largely focused on PARP1 and the closely related PARP2, but recent work highlighting the role of another family member, tankyrase 1 (TANK1; also known as PARP5A and ARTD5), in the control of WNT signalling has fuelled interest in the development of additional inhibitors to target this enzyme class. Tankyrase function is also implicated in other processes such as the regulation of telomere length, lung fibrogenesis and myelination, suggesting that tankyrase inhibitors could have broad clinical utility. Here, we discuss the biology of tankyrases and the discovery of tankyrase-specific inhibitors. We also consider the challenges that lie ahead for the clinical development of PARP family inhibitors in general.