Virtually everyone believes that we have a duty to rescue fellow human-beings from serious danger when we can do so at small cost to ourselves – and this often forms the starting point for arguments in moral and political philosophy on topics such as global poverty, state legitimacy, refugees, and the donation of body parts. But how are we to explain this duty, and within what limits does it apply? It cannot be subsumed under a wider consequentialist requirement to prevent harm. Nor can it be understood as a duty of social justice that citizens owe to one another under a social contract for mutual protection. Instead it is a sui generis duty of justice that arises from the direct physical encounter between rescuer and victim, and is accordi...