Quantum hydrodynamic (QHD) models study hydrodynamic phenomena where quantum effects must be taken into account, such as superfluidity, Bose-Einstein condensation, quantum plasmas, or semiconductor devices. In this talk, I will give a briefly introduction on the physical background of several QHD models, as well as some related mathematical problems and their literatures. Last, I will introduce some recent results about the 1-dimensional collisional Quantum Hydrodynamics (QHD) system and its relaxation-time limit, which is a work in collaborating with Paolo Antonelli and Pierangelo Marcati.