The entanglement structure in quantum systems is important for both fundamental and application reasons. One of the schemes to achieve non-trivial entanglement structures is through systems with local constraints. In equilibrium, the local constraints could qualitatively change the wave function's product state nature and achieve exotic quantum many-body states with anyon statistics. In addition to non-trivial entanglement structure, local constraints can also lead to novel real-time dynamics such as disorder-free localization. In this talk, I will introduce my works and discuss recent developments in the study of constrained quantum many-body systems in equilibrium and real-time evolutions.