The theory of Yangians was introduced by Drinfeld in the 1980s as a systematic approach to solving the Yang-Baxter equation: every irreducible finite-dimensional representation is proved to be equipped with a rational R-matrix obtained by normalising the action of the universal R-matrix. Drinfeld's proof of the existence of the universal R-matrix for the Yangian of finite type was non-constructive and cohomological in nature. More recently, Gautam, Toledano Laredo, and Wendlandt proposed an alternative explicit construction. In this talk, I will give an overview of these results and present a generalisation for the Yangian of affine type. This is based on a joint work with S. Gautam and C. Wendlandt.