Major statistical properties for 2-d hyperbolic systems have been well understood recently, based upon fundamental work of Sinai, Bunimovich, Chernov, Young and many others. I will go over some categories of diffusive hyperbolic systems, which includes classical billiards, billiards under random or deterministic perturbations, systems with micro-geometric structure; time-dependent billiards. Some physical laws related to nonequilibrium systems with physical origin will also be reviewed.