During this talk, the capabilities of the relaxation time approximation (RTA) for the Boltzmann collision integral are assessed in the context of some benchmark problems. After briefly introducing the quadrature techniques employed for numerical computations, the following applications are summarised:

• Van der Waals and Cahn-Hilliard models for multiphase and multicomponent flows.
• Rarefied gas flows through micro-channels: RTA vs DSMC for Maxwell molecules and ab initio potentials, in the context of planar Couette flow.
• Shock wave propagation: RTA vs DSMC for hard spheres and ab initio potentials, in the standing shock problem.
• Relativistic fluid dynamics: longitudinal wave damping and relativistic transport coefficients; RTA vs BAMPS for planar shock wave propagation; Bjorken flow.