Both classical and contemporary literature are filled with descriptions of situations that are supposed to be moral dilemmas or unresolvable conflicts between strong moral requirements. The best known examples are Greek tragedies, such as those about Antigone and Agamemnon, and Shakespearian tragedies, but many recent novels, such as Sophie's Choice, also hinge on moral dilemmas. These stories are so common and so realistic that they seem to show that moral dilemmas can occur. This impression is also supported by everyday experience. Almost everyone has faced some situation where each of two incompatible alternatives is favoured by some strong moral requirement, but there seems to be no objective way to resolve the conflict. Such situations seem to be common not only for those who determine which people will die, such as doctors and military personnel, but also for anyone with divergent commitments — for example, to friends, family and country. All of this makes it a matter of common sense that moral dilemmas are possible and even actual. Nonetheless, philosophers often deny common sense. Philosophers have denied that time is real, that anyone can know anything, that anyone has free will, that minds are distinct from bodies, and much else that seems to be common sense. They claim to have strong arguments that common sense is not always as reliable as it seems. Similarly, most traditional moral philosophers deny that unresolvable moral dilemmas can ever really occur. They realize that they are denying common sense, so they give a variety of arguments against moral dilemmas. They assume that the purpose of a moral theory is to give a procedure for deciding what to do in every moral situation, so the best moral theory must show either that moral requirements never really conflict or that such conflicts are always resolvable by finding the one right action. This view is shared by most utilitarians and many of their rival deontologists, such as Aquinas and Kant. And this tradition is still alive today. Of course, philosophers do not all agree about the possibility of moral dilemmas (or anything else). Even though traditional philosophers deny the possibility of moral dilemmas, other philosophers have recently rejected the philosophical tradition and argued that moral dilemmas are actual or at least possible. Sartre was one of the first to be so bold. Several deontic logicians later reached similar conclusions by very different methods. These philosophers not only defend common sense but also claim that the possibility of moral dilemmas is important for several reasons. First, moral dilemmas force us to rethink the traditional view of the nature and purpose of moral theory and thus of the standards for deciding among moral theories. Traditional moral philosophers often assume that a moral theory must provide a complete moral decision procedure, but such completeness cannot be attained if moral dilemmas cannot be resolved. The recognition of moral dilemmas can thus prevent unrealistic expectations that distort moral theories and lead some to reject the whole project of ethics. Some defenders of moral dilemmas also claim that the possibility of moral dilemmas refutes realism, objectivism, absolutism or rationalism in morality. Other moral philosophers have responded that moral dilemmas not only do not refute moral realism but actually support it. If either claim is correct, the possibility of moral dilemmas might solve one of the oldest and most important debates in moral philosophy. The possibility of moral dilemmas also provides a new way to think about concrete moral problems. When a moral philosopher asks questions such as whether a preferential treatment programme is morally permitted, it is often assumed that there are only two alternatives. Either the preferential treatment programme is required, because the rights of those who benefit override the rights of those who are excluded; or the programme is not permitted, because the rights of those who are excluded override the rights of those who benefit. The recognition of moral dilemmas provides another alternative: neither right overrides the other, so the conflict is unresolvable. There is still much to be said about what can and should be done and felt in such situations, but this discussion cannot even begin until the possibility of moral dilemmas is admitted. These philosophical implications and others make it important to determine whether moral dilemmas are possible. But moral dilemmas also have an intrinsic interest of their own. If moral dilemmas are as common as it seems, each of us will probably face some moral dilemma in his or her own personal life. We can deal with these situations better when they arise if we understand their nature and implications in advance. All of this makes it worthwhile to make the considerable effort that is needed to understand these complex situations.