We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate mu, while at the same time a random walker moves on G at rate 1, but only along edges which are open. On the d-dimensional torus with side length n, when the bond parameter is subcritical, we determined (with Y. Peres and A. Stauffer) the mixing times for both the full system and the random walker. The supercritical case is harder, but using evolving sets we were able (with Y. Peres and P. Sousi) to analyze it.