  In this survey, we shall be concerned with the category of finite-dimensional
representations of the untwisted quantum affine algebras when the quantum
parameter q is not a root of unity. We review the foundational results of the
subject, including the Drinfeld presentation, the classification of simple
modules and q-characters. We then concentrate on particular families of
irreducible representations whose structure has recently been understood:
Kirillov-Reshetikhin modules, minimal affinizations and beyond.
