In this talk, we focus on the free boundary regularity in the one-phase Stefan problem. Specifically, we describe a recent perturbative approach to the study of this. In the first part, we introduce some general notions and results connected with free boundary problems. In the second part, we deal with the specific topic of the talk, providing the key steps of the method. This talk is based on a joint work with D. De Silva and O. Savin.