  This article is an extended version of the minicourse given by the second
author at the summer school of the conference "Interactions of quantum affine
algebras with cluster algebras, current algebras and categorification", held in
June 2018 in Washington. The aim of the minicourse, consisting of three
lectures, was to present a number of results and conjectures on certain
monoidal categories of finite-dimensional representations of quantum affine
algebras, obtained by exploiting the fact that their Grothendieck rings have
the natural structure of a cluster algebra.
