 There is wide agreement that a term is vague to the extent that it has borderline cases. This makes the notion of a borderline case crucial in accounts of vagueness. This entry will concentrate on an historical characterization of borderline cases that most commentators still accept. Vagueness will then be contrasted with ambiguity and generality. This will clarify the nature of the philosophical challenge posed by vagueness. The entry will then discuss some rival theories of vagueness with an emphasis on many-valued logic, supervaluationism and contextualism. In the penultimate section this entry will discuss Kit Fine’s (2020) holistic challenge to the logical possibility of a borderline case. The entry concludes with the issue of whether all vagueness is linguistic.