Abstract: The rarefaction effects arise when the mean free path of gas molecules is comparable to the characteristic flow length. Compared to monatomic gas, the dynamics of rarefied molecular gas, which consists of two or more atoms in one gas molecule, is more complicated, due to the additional non-equilibrium effects in the rotational and vibrational motions. As the major constituent in the atmosphere of Earth and Mars, rarefied molecular gas dynamics has strong applications in aerospace science, micro-electro-mechanical system, shale gas extraction, and so on. However, the corresponding models and simulation methods are not sophisticated. Starting from the monatomic gas and the Boltzmann equation, we review the development of the kinetic modeling of rarefied gas and the essential connection between the transport coefficients and relaxation processes. Then, we focus on the relaxation process and transport coefficients of molecular gas, and introduce typical kinetic models with the systematic assessment of their accuracy. Meanwhile, we discuss the defect of direct simulation Monte Carlo method in the modeling of rarefied molecular gas, i.e., it cannot specify the thermal relaxation rates (hence cannot recover the thermal conductivities) when the bulk viscosity is determined. Finally, we use the Wu model to quantify the uncertainties, and discuss how to reduce or even eliminate the uncertainties based on the data from the molecular dynamics simulation and Rayleigh-Brillouin scattering experiment. This present article is instructive for the modeling of rarefied gas flows involving chemical reactions.