Abstract: Convergence of the Cardy-Smirnov observables is the crucial part of the famous proof of existence of the scaling limit of critical percolation on hexagonal lattice. I will discuss a proof of the power law convergence of Cardy-Smirnov observables on arbitrary simply-connected planar domains. The proof works for the usual critical percolation on hexagonal lattice, as well as for some modified versions. In the heart of the proof lies a careful study of the fine boundary properties of arbitrary planar domains. I will also explain the relevance of this result for the investigation of the rate of convergence of the critical percolation to its scaling limit. This is a joint work with L. Chayes and H. K. Lei.