During the last couple of decades, several attempts have been made to come up with a theory that can handle the various semantic, logical and philosophical problems raised by the vagueness of natural languages. One of the most influential ideas that have come into fashion in recent years is the idea that vagueness should be analysed as a form of context sensitivity. Such contextualist theories of vagueness have gained some popularity, but many philosophers have remained sceptical of the prospects of finding a tenable contextualist solution to the problems of vagueness. This paper provides an introduction to the most popular contextualist accounts, and a discussion of some of the most important arguments for and against them.