I will describe recent advances in the Pugh-Shub stable ergodicity theory for partially hyperbolic diffeomorphisms. In particular, I consider two "competing" methods to show that a given partially hyperbolic diffeomorphism is stably ergodic (i.e., it is ergodic along with any of its sufficiently small perturbations). One of them relates the problem to to the global estimates of the action of the system along its central direction while another one deals with a more delicate estimates using Lyapunov exponents in the central direction.