There is no single “problem of punishment”. The activity of punishing is problematic at many levels. There are problems relating to the authority to punish, the severity of punishment, the method of punishment, and of course the moral basis for punishment. Given this, we should be surprised were we to find that all these problems could be comprehended by a single, simple rationale. Nevertheless, there is one, fundamental, underlying moral challenge posed by all punishment, and it is especially (though not exclusively) to this that the classical justifications of punishment have been primarily directed. “Retributivist” and “utilitarian” justifications, however we understand them, are, above all, responses to what I see as this central problem of punishment.