Tensor network states have established themselves as the natural language based on entanglement to describe and numerically simulate quantum many-body systems. In this talk I will first provide a long introduction to what tensor network states are, as well as to some of their related numerical methods. An overall perspective on the field will also be provided. Then, I will review recent progress on this topic conducted in my group. In particular, I will focus on the study of (i) 2d topological order, and (ii) Kagome Heisenberg antiferromagnets on a field, but other relevant developments may also be briefly discussed. Finally, I will discuss future research directions including the role of tensor networks in AdS/CFT, lattice gauge theories, many-body localization, and other recent ideas.