Appears in collection : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

The Feigenbaum point is a remarkable parameter in the quadratic family focusing some of the deepest phenomena of non-linear dynamics (regular vs chaotic behavior, rigidity and MLC, universal self-similarity and renormalization). A theory of this point has been under construction for about 45 years. I will outline this story, completing it with one missing piece, MLC at this point (based on a joint work with Dima Dudko).