In this talk, I will provide an introduction into the area of extended formulations. I will also present the results from the seminal paper “Expressing combinatorial optimization problems by Linear Programs” by Yannakakis, which is central for the study of extended formulations for combinatorial problems. We will go through the proof of Yannakakis theorem about the relationship between extension complexity of a polytope and the nonnegative rank of its slack matrix. We also show how this theorem generalizes to extensions based on SDP cones. We will also discuss the implications of this theorem for stable sets polytope of perfect graphs.