In the first part of this introductory talk, I will give you a hint of how and why the area of linear lifts of polytopes (AKA linear extended formulations) came into being. Starting with Yannakakis' fundamental contribution, which laid dormant for too long, I will take you to the results that revived the interest in lifts of polytopes. In the second part, I will explain some of the many connections that sustain the area, the amazing results that have been obtained recently, the open problems that remain, and the barriers that stand in our way.