The purpose of this talk is to give an overview on recent progress in exactly solvable 2-dimensional lattice models of statistical mechanics. I will discuss the Yang-Baxter equation, star-triangle relation and their properties. Then I will present new solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations. These solutions are expressed in terms of hypergeometric functions. If time permits I will discuss the relationship between Yang-Baxter equation and supersymmetric dualities.