After the fourth moment theorem, many results on the Wiener chaos are obtained as an application of Stein's method and Malliavin calculus. For example, the estimate of distances between a given distribution and the normal distribution, the rate of convergence of a sequence in the Wiener chaos, and Berry–Esseen type bounds. In this talk, we consider Stein's equations with respect to invariant measures of diffusion processes, and discuss estimates of distances between a given distribution and the invariant measures and convergence of distributions to the invariant measures. This talk is based on the joint work with Ciprian Tudor.