The conceptualization and moral analysis of discrimination constitutes a burgeoning theoretical field, with a number of open problems and a rapidly developing literature. A central problem is how to define discrimination, both in its most basic direct sense and in the most prominent variations. A plausible definition of the basic sense of the word understands discrimination as disadvantageous differential treatment of two groups that is in some respect caused by the properties that distinguish the groups, but open questions remain on whether discrimination should be restricted to concern only particular groups, as well as on whether it is best conceived as a descriptive or a moralized concept. Furthermore, since this understanding limits direct discrimination to cases of differential treatment, it requires that we be able to draw a clear distinction between equal and differential treatment, a task that is less simple than it may appear, but that is helpful in clarifying indirect discrimination and statistical discrimination. The second major problem in theorizing discrimination is explaining what makes discrimination morally wrong. On this issue, there are four dominant contemporary answers: the valuational and expressive disrespect accounts, which hold that discrimination is wrong when and if the discriminator misestimates or expresses a misestimate of the moral status of the discriminatee; the unfairness account, which holds that discrimination is wrong when and if the discriminator unfairly increases inequality of opportunity; and the harm account, which holds that discrimination is wrong when and if the discriminator harms the discriminatee. Each of these accounts, however, faces important challenges in simultaneously providing a persuasive theoretical account and matching our intuitions about cases of impermissible discrimination.