Block models are random graph models which have been extensively studied in statistics and theoretical computer science as models of communities and clustering. A conjecture from statistical physics by Decelle et. al predicts an exact formula for the location of the phase transition for statistical detection for this model. I will discuss recent progress towards a proof of the conjecture. Along the way, I will outline some of the mathematics relating a popular inference algorithm named belief propagation, the zeta functions of random graphs and Gibbs measure on trees. Based on joint works with Joe Neeman and Allan Sly.