The introduction by Schramm in 1999 of the Stochastic Lowner Evolution (now rather known as Schramm-Loewner Evolution or simply SLE) led to some of the most spectacular recent progress in the study of critical two-dimensional statistical physics models. The construction of SLE involves both probabilistic techniques and tools from complex analysis; the goal of this talk is to give a mostly self-contained introduction to this process, as well as to some of the results that were later proved using it as a tool. I will also mention a few related question that remain open.