This paper features two main contributions. On the one hand, it gives an impressive survey on the progress on the diameter problem, including the breakthrough of the author with his disproof of the Hirsch conjecture among many other recent results. On the other hand, it features new results (exponential lower bounds) on the diameter of simplicial complexes and re-interprets the recent activities of the polymath 3 project that has been coordinated by Gil Kalai.