In this Chapter, the performance of the moment methods, in terms of accuracy and computational efficiency, is evaluated at both the macro- and microscopic levels. Three different types of non-equilibrium gas flows, including the force-driven Poiseuille flow, lid-driven and thermally induced cavity flows, are simulated in the slip- and transition regimes. Choosing the flow fields obtained from the Boltzmann model equation as the benchmark, the accuracy and validation of Navier-Stokes-Fourier (NSF), regularized 13 (R13) and regularized 26 (R26) equations are explored at the macroscopic level.