The Hippo pathway and its downstream effectors, the transcriptional co-activators Yes-associated protein (YAP) and transcriptional co-activator with PDZ-binding motif (TAZ), regulate organ growth and cell plasticity during animal development and regeneration. Remarkably, experimental activation of YAP/TAZ in the mouse can promote regeneration in organs with poor or compromised regenerative capacity, such as the adult heart and the liver and intestine of old or diseased mice. However, therapeutic YAP/TAZ activation may cause serious side effects. Most notably, YAP/TAZ are hyperactivated in human cancers, and prolonged activation of YAP/TAZ triggers cancer development in mice. Thus, can the power of YAP/TAZ to promote regeneration be harnessed in a safe way? Here, we review the role of Hippo signalling in animal regeneration, examine the promises and risks of YAP/TAZ activation for regenerative medicine and discuss strategies to activate YAP/TAZ for regenerative therapy while minimizing adverse side effects.