Cluster algebras are special kinds of commutative algebras introduced by Fomin and Zelevinsky in the early 2000s. Since their introduction, a lot of connections and applications have been discovered in various fields of mathematics. A monoidal category is called a monomial categorification of a given cluster algebra,  according to Hernandez and Leclerc,  if its Grothendieck ring is isomorphic to the cluster algebra and every cluster monomials corresponds to a simple object in the category.   In this talk, I will explain our results on the monoidal categorification of cluster algebras via subcategories of representations of quantum affine algebras, including a criterion for a monoidal subcategory of finite-dimensional modules of quantum affine algebra  to become a monoidal categorification of its Grothendieck ring. This is joint research with Masaki Kashiwara, Se-jin Oh, and Euiyong Park.