We discuss the rate of convergence of the critical interfaces of various critical lattice models to SLE. In particular, we examine the exploration process for the critical percolation. We talk about the fact that for any "reasonable" critical percolation model for which the convergence of the exploration process is established, the polynomial rate of convergence must automatically hold. So far, the result is unconditional for the critical site percolation on the hexagonal lattice and for some of its generalizations, which will be discussed at the talk. We also analyze a general framework for establishing these types of results for other models. The talk is based on joint projects with L. Chayes, H. Lei, and L. Richards.