This paper considers the problem of plagiarism as an issue of morality. Outrage about student plagiarism in universities positions it as dishonesty and a transgression of standards. Despite this, there has been little work analysing the implications of positioning plagiarism as a moral matter in the making of judgments about plagiarism and academic dishonesty. This paper sets the scene by reviewing research about the characteristics of students who cheat and analysing student and lecturer differences. It then discusses perspectives from moral behaviour, moral philosophy and moral reasoning. The paper concludes that emotion and reason are brought to moral judgments, and so makes a case for those who are making judgments about plagiarism to reflect on whether they are faced with a matter of morality or convention. Greater awareness of the domains of convention and morality, the issues of justice and care, the roles of emotion and reason and what is involved in making judgments, will open ways of understanding reactions to plagiarism so that better ways to deal with accusations and make judgments can be developed.