In this talk I will introduce Schramm-Loewner Evolutions (SLE) theory and I will discuss some PDEs that appear naturally in this study. I will spend most of the time on a specific PDE that models a fundamental quantity in SLE theory: the density of the law of the SLE tip. I will present a series of recent results on this object based on the analysis of this PDE, obtained jointly with Yizheng Yuan and Oleg Butkovksy, as well as some open problems. I will also describe the progress of the SLE community in the study of a different PDE and describe some open problems as an invitation to the community for further discussions!