Hilbert expansion and Chapman-Enskog method build the linkage between mesoscopic Boltzmann equation and macroscopic Euler and Navier-Stokes equation. However, these methods only give formal expansion and lack of rigorous mathematical proof. In this talk, I will discuss the physical background of the hydrodynamic limit of Boltzamnn equation and review some successful proof of convergence of the Boltzmann equation towards a Navier- Stokes system.