Representations of quantum affine algebras in their $R$-matrix realization

We use the isomorphisms between the $R$-matrix and Drinfeld presentations of the quantum affine algebras in types $B,C$ and $D$ produced in our previous work to describe finite-dimensional irreducible representations in the $R$-matrix realization. We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the $R$-matrix and Drinfeld presentations of the Yangians.