A moral dilemma is a situation in which a person cannot avoid acting wrongly. In the first part of the dissertation, I examine the two most important arguments for the possibility of moral dilemmas: the incommensurability argument and the argument from guilt. I argue that neither of these arguments is successful. In the second part of the dissertation, I show that moral dilemmas are a species of moral luck, or moral responsibility for factors beyond one's control. I argue that those who believe in the possibility of moral dilemmas must also accept the possibility of some kinds of moral luck. This result holds even for moral dilemmas secundum quid, or dilemmas that arise only as a result of prior wrongdoing. In the final part of the dissertation, I consider several arguments for the possibility of circumstantial moral luck. I argue that these arguments all fail; however, I acknowledge that there may be other, more compelling arguments for the possibility of moral luck. I conclude by suggesting that the most important objection to moral dilemmas and moral luck is rooted in a concern for justice.