The Boltzmann equation, when the gas is out of equilibrium, is an hard mathematical problem which is unresolved apart from very exceptional situations. The kinetic theory of non-uniform elastic gases near equilibrium, mainly due to Sydney Chapman and David Enskog [62], has been successful in establishing a method to derive the transport coefficients from the Boltzmann equation, obtaining closed hydrodynamic equations. It is interesting to mention that the first non-equilibrium solutions of the Boltzmann equation were presented by Enskog in his Ph.D thesis [80], defended in 1917 at the University of Uppsala, Sweden. In the late 40s H. Grad [99] developed an alternative mathematically equivalent method to obtain the same results. In this section we review the main passages of the kinetic theory of non-equilibrium elastic gases in order to have a reference frame for the next section, where the granular kinetics will be presented.