following smirnov’s proof of cardy’s formula and schramm’s discovery of sle, a thorough understanding of the scaling limit of critical percolation on the regular triangular lattice the has been achieved. smirnorv’s proof in fact gives a discrete approximation of the conformal embedding which we call the cardy embedding. in this talk i will present a joint project with nina holden where we show that the uniform triangulation under the cardy embedding converges to the brownian disk under the conformal embedding. moreover, we prove a quenched scaling limit result for critical percolation on uniform triangulations. time permitting, i will also explain how this result fits in the the larger picture of random planar maps and liouville quantum gravity