Given a natural number n and a graph H, the extremal number ex(n, H) is the largest number of edges in an H-free graph on n vertices. One of the outstanding questions concerning extremal numbers, originally posed by Erdos and Simonovits, is the rational exponents conjecture, which asks whether for every rational number r between 1 and 2, there is a graph H such that c n^r < ex(n, H) < C n^r for some positive constants c and C. We will discuss some of the recent progress on this conjecture.