  These notes reflect the contents of three lectures given at the workshop of
the 14th International Conference on Representations of Algebras (ICRA XIV),
held in August 2010 in Tokyo. We first provide an introduction to quantum loop
algebras and their finite-dimensional representations. We explain in particular
Nakajima's geometric description of the irreducible q-characters in terms of
graded quiver varieties. We then present a recent attempt to understand the
tensor structure of the category of finite- dimensional representations by
means of cluster algebras.
