Abstract: We review the development of numerical renormalization group methods, including Wilson's numerical renormalization group,White's density matrix renormalization group, and several recent rapidly developing tensor network state-based algorithms. Among these, particular emphasis is laid on the linearized tensor renormalization group method, which was recently proposed to accurately calculate the thermodynamic properties of quantum many-body lattice systems, and which may have broad applications in both one- and two-dimensional quantum systems.