Dynamics in the family e^{2\pi i \theta} z + z^2 is one of the most delicate themes of Holomorphic Dynamics. Three regimes, parabolic, Siegel and Cremer, are intertwined in an intricate way depending on the Diophantine properties of the rotation number \theta. Global structure of Siegel maps of bounded type is now well understood due to the methods of quasiconformal surgery and renormalization. On the other hand, the structure of maps of high type is also well understood by means of parabolic renormalization. Recently new methods of Near Degenerate Regime have been developed giving a chance for complete understanding of this family. In the talk we will give a self-contained overview of this story.