The concept and methodology of the renormalization group is a cornerstone in physics, with far-reaching implications for the study of quantum field theory and critical phenomena. Its impact on the field cannot be overstated. One important direction in the research of many-body quantum theory is the renormalization group study of the so-called tensor-network states. The ultimate goal is to provide a powerful tool for solving correlated quantum problems, such as the mechanism behind high-temperature superconductivity. In this talk, I will delve into the physical background and fundamental ideas that underlie the development of this field. Additionally, I will discuss the latest progress and explore directions for future research. Through this exploration, we hope to gain a deeper understanding of the renormalization group and its potential for further advancing our understanding of the complex phenomena that arise in quantum many-body systems.