I will first review the relation among diffusion processes, solutions of diffusion equations, and billiard systems, essentially though the FeynmanKac formula. Major statistical properties for 2-d hyperbolic systems have been well understood recently. Several categories of diffusive hyperbolic systems will be reviewed, which includes classical billiards, billiards under random or deterministic perturbations, systems with micro-geometric structure; timedependent billiards. If the system has a physically interesting steady state, then it belong in the class of ergodic SRB measures and their modifications. Some Physical laws that are related to nonequilibrium billiards with physical origin will also be discussed.