In this talk, we will present a mathematical model for the description of granular mixtures. Granular gases consist of collections of macroscopic particles, that interact through energy-dissipating collisions. Such inelastic behavior of collisions is characterized by conservation of mass and total momentum, but dissipation of kinetic energy. The system is modeled by a Boltzmann-type kinetic equation, describing a gas mixture composed of different species, each with its own mass. We will analyze the Boltzmann-type equation by providing Povzner-type inequalities and developing Cauchy theory in general Orlicz spaces, inspired by the single-species framework. The large time behavior of the solution will be investigated, revealing a mixture analogue of the seminal Haff’s Law. In this context, suitable and efficient fast spectral methods have been developed to numerically approximate the collision operator. Numerical simulations will be provided to validate theoretical results and to explore the behavior of solutions in different scenarios.