It was a classical problem going back to Fatou of whether a Julia set of a polynomial may have positive area. It was realized in the 1980s that it is intimately related to the problem of ``wild" attractors. Examples of entire functions of this kind were constructed in the 1980s, but it took another 20 years to produce polynomial ones. First examples, of Cremer polynomials, were constructed by Buff and Cheritat. More abunndant and robust class of examples, of Feigenbaum polynomials, was later produced by Avila and the author. Moreover, these maps admit a perturbation to polynomial automorphisms of C^2. The whole story is based upon several renormalization theories that allow one to control precisely small scale geometry of various dynamical systems and bifurcation loci.