The first part of my talk will be devoted to an overview of recent developments about Yangians and their connections to other interesting mathematical objects. Afterwards, it will be explained how to construct a coproduct on a certain completion of the Yangian attached to an affine Kac-Moody algebra. Vertex operator representations of Yangians will also be introduced: they are the analogs of the vertex operator representations of quantum affine algebras due to I. Frenkel and N. Jing. One application of these representations to the structure of Yangians will be presented.