Hernandez-Leclerc categories take an important position in study of quantum affine algebras and cluster algebras. In this talk, I will talk about the quantum Grothendieck ring of Hernandez-Leclerc category. The first part will be devoted to explaining the definition of the quantum Grothendieck ring and its ring-theoretic properties. Then I will talk about my recent work on the PBW theory for the quantum Grothendieck ring, which is based on arXiv:2401.04878.