The challenge of the chiral Potts model
  The chiral Potts model continues to pose particular challenges in statistical mechanics: it is ``exactly solvable'' in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later.   However, a derivation of that conjecture had to wait until 2005. Here we discuss that derivation. 
R.J. Baxter