Rodney Baxter has succeeded in giving exact solutions to a variety of problems in statistical mechanics. Their significance lies in the test they offer of any general framework solutions to statistical thermodynamics. In this respect, they have played a role similar to that of Lars Onsager’s solution of the two-dimensional Ising model, 70 years ago. The solution of such classical problems as the eight-vertex model and the Potts model, and the discovery of models whose critical indices vary with interaction parameters are major contributions to the mathematical framework of physics and chemistry. This work gained Rodney the Boltzmann Prize of the IUPAP for 1980.