An overview of recent results pertaining to the hydrodynamic description (both Newtonian
and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic
Maxwell models is presented. The use of this mathematical model allows us to get exact
results for different problems. First, the Navier–Stokes constitutive equations with
explicit expressions for the corresponding transport coefficients are derived by applying
the Chapman–Enskog method to inelastic gases. Second, the non-Newtonian rheological
properties in the uniform shear flow (USF) are obtained in the steady state as well as in
the transient unsteady regime. Next, an exact solution for a special class of Couette
flows characterized by a uniform heat flux is worked out. This solution shares the same
rheological properties as the USF and, additionally, two generalized transport
coefficients associated with the heat flux vector can be identified. Finally, the problem
of small spatial perturbations of the USF is analyzed with a Chapman–Enskog-like method
and generalized (tensorial) transport coefficients are obtained.