Sexism occurs when men are believed to be superior to women, and is thought to be one of the reasons for women's underrepresentation in physics and astronomy. The issue of sexism in physics and astronomy has not been thoroughly explored in the physics education literature and there is currently no clear language for discussing sexism in the field. This article seeks to begin a conversation on sexism in physics and astronomy and offer a starting point for language to discuss sexism in research groups and departments. Interviews with 21 women in graduate physics and astronomy programs are analyzed for their individual experiences of sexism. Although a subset of women did not report experiencing sexual discrimination, the majority experienced subtle insults and slights known as microaggressions. Other participants also experienced more traditional hostile sexism in the form of sexual harassment, gender role stereotypes, and overt discouragement. These results indicate the existence of sexism in the current culture of physics and astronomy, as well as the importance departments must put on eliminating it and educating students about sexism and microaggressions. [This paper is part of the Focused Collection on Gender in Physics.]