Real rank zero plays an important role in classification as counterexamples to Elliott's conjecture seem to fail to have real rank zero. I will talk about the conditions on a 2-graph ? that are necessary and sufficient for the associated C*-algebra $C^*(\Lambda)$ to have real rank zero. A complete answer is obtained when $C^*(\Lambda)$ is purely infinite. This is joint work with Aidan Sims and David Pask.