  We make a brief historical review to the moment model reduction to the
kinetic equations, particularly the Grad's moment method for Boltzmann
equation. The focus is on the hyperbolicity of the reduced model, which is
essential to the existence of its classical solution as a Cauchy problem. The
theory of the framework we developed in last years is then introduced, which
may preserve the hyperbolic nature of the kinetic equations with high
universality. Some lastest progress on the comparison between models
with/without hyperbolicity is presented to validate the hyperbolic moment
models for rarefied gases.

Statistical Mechanics;Computational Physics;Fluid Dynamics