I'm thinking of topics to discuss over the summer with students here, and decided on introducing people to complexity theory via the question, "Why haven't we solved the P vs NP problem?". The title is a little tongue-in-cheek: the real idea is to use P vs NP to explore some concepts in complexity theory, for an audience that has no real familiarity with the topic.
Thus far, I'm working off the "diagonalization-oracles-boolean-circuits-razborov-rudich" story line, with an addition at the end for algebraization, and P vs NC. But since this isn't my real area of expertise, I'm throwing out a request for suggestions: what topics am I missing when discussing the various attacks on P vs NP ?
p.s I'm using Scott Aaronson's P vs NP survey as a rough starting guide for references.