The primary aim of this paper is to expound G.E.M. Anscombe’s remark that “I” is not a referring term.  Part of the difficulty of this remark is to know what it means.  Anscombe is clear that she does not deny the rule: “If X asserts something with ‘I’ as subject, his assertion will be true if and only if what he asserts is true of X”.  If Anscombe is not denying this, what is she denying?  This paper seeks to answer this question, by understanding her remark against the background of a broadly Fregean conception of reference, specifically the neo-Fregean conception developed by Gareth Evans.  It suggests that Anscombe and Evans mean the same thing by a “referring term”, namely, a term whose use is an exercise of a way of thinking that contains identifying knowledge of which object is being thought of.  Evans thinks that “I” is a referring term in this sense, and he calls the way of thinking associated with its use “self-identification”.  The point of Anscombe’s remark is to deny that there is any such thing as self-identification.  The second aim of this paper is to explain why Anscombe seems to be right about this, and to do something to explore the philosophical significance of this fact.