Clinicians and health researchers frequently encounter opportunities to rescue people. Rescue cases can generate a moral duty to aid those in peril. As such, bioethicists have leveraged a duty to rescue for a variety of purposes. Yet, despite its broad application, the duty to rescue is underanalysed. In this paper, we assess the state of theorising about the duty to rescue. There are large gaps in bioethicists' understanding of the force, scope and justification of the two most cited duties to rescue--the individual duty of easy rescue and the institutional rule of rescue. We argue that the duty of easy rescue faces unresolved challenges regarding its force and scope, and the rule of rescue is indefensible. If the duty to rescue is to help solve ethical problems, these theoretical gaps must be addressed. We identify two further conceptions of the duty to rescue that have received less attention--an institutional duty of easy rescue and the professional duty to rescue. Both provide guidance in addressing force and scope concerns and, thereby, traction in answering the outstanding problems with the duty to rescue. We conclude by proposing research priorities for developing accounts of duties to rescue in bioethics.