We will overview the dynamical picture of the real quadratic family, viewed as a slice of the complex one, that has recently been completed with a theorem (joint with Dima Dudko and Jeremy Kahn) confirming local connectivity of the Mandelbrot set M along the real line. It implies a uniform qc control of the real symmetric Mandelbrot copies and has

ramifications related to the structure of the Full Renormalization Horseshoe and associated self similarity features of M.