Abstract: The convergence of critical lattice interfaces to Schramm–Loewner Evolution is a central topic in two‑dimensional probability, with foundational contributions by Greg Lawler. In this talk, I will discuss recent progress on quantitative versions of this convergence, focusing on polynomial rates at which discrete interfaces approach their SLE limits. I will present a general framework that yields power‑law convergence rates under natural regularity assumptions, providing a unified approach that applies to a wide class of lattice models. As a main example, I will consider the exploration process in critical percolation and show that, for any suitably well‑behaved critical percolation model, convergence to SLE holds together with an automatic polynomial rate. In particular, this result applies unconditionally to critical site percolation on the hexagonal lattice and to several of its generalizations. I will also briefly explain how the same framework extends to other models, including the Harmonic Explorer and the critical Ising model. This talk is based on joint work with L. Chayes, D. Chelkak, H. Lei, and L. Richards.