This is a survey paper in the study of reaction-diffusion processes. Schögl's model and Brussel's model are presented in the first section, they are typical models in non-equilibrium statistical physics. The case of a finite number of sites is not so easy, but is now quite well understood. The construction of the process which is associated with an infinite number of sites is very hard. A useful tool in this way is the Markovian coupling. Existence of stationary distributions, ergodicity and phase transitions are discussed. When the formal generator of the process is suitably rescaled, we are lead to the reaction-diffusion equation which describes the macroscopic behavior of the physical system.