We consider the stochastic quantization equation in 3 dimensions,

which has been formally defined to describe the dynamics whose stationary distribution is the \phi^4_3 measure arising in the Euclidean quantum field theory. Considering finite difference approximations of this equation, using the theory of regularity structures and exploiting an argument a-la Bourgain (for the non-linear Schroedinger equation), we prove that the \phi^4_3 measure is indeed invariant for this dynamics. This is a joint work with Martin Hairer.