Statistical physicists have conjectured that the scaling limits of many two-dimensional lattice models are in some sense conformally invariant. These scaling limits can be described using one well-known tool, Brownian motion and the SLE process. One of the application of this theory is the computation of the exact value of the Hausdorff dimension of some exceptional sets about planar Brownian motion. In this seminar, we will focus on the introduction of the SLE process and its connection to the discrete models.