Periodic Lorentz gases are particular cases of a general framework of Z^d-cover of hyperbolic dynamical system. In this context, the rate of mixing is directly related to the local limit theorem of the step function. This enables us, when the horizon is finite, to obtain an mixing expansion of every order for the collision map, but also for the flow. Contrarily to previous expansions obtained in other contexts of dynamical systems preserving an infinite measure, the coefficients appearing in our expansion are linearly independent. This provides in particular mixing rate for null integral observables. The result for the flow (in the finite horizon case) is a recent joint work with Dmitry Dolgopyat and Péter Nándori. In the more complicated case of infinite horizon, error terms in mixing estimates for the collision map, including results for some null integral observables, have been obtained very recently in a joint work with Dalia Terhesiu.