Abstract: Does the Constitution guarantee free speech on university campuses? The Supreme Court has essentially said so, at least insofar as we are speaking of public universities. Some private universities are interested in adhering to the First Amendment, even though it does not bind them. But what do First Amendment protections entail or require? It is clear that in general, universities may not discriminate on the basis of viewpoint. It is also clear that as educational institutions, universities may sometimes regulate speech to protect their essential mission – by, for example, forbidding “true threats,” prohibiting plagiarism, protecting speakers from being shouted down, forbidding students from taking over buildings, and ensuring that students and teachers focus on the topics of their courses. By exploring thirty-seven scenarios, it is possible to concretize these general propositions, and to see which questions are easy and which questions are hard. The broadest conclusion is that to the extent that universities seek to comply with the First Amendment, they must permit a great deal of speech that is offensive, hateful, and even horrifying.