1D Holomorphic Dynamics (in a narrow sense) is the theory of iteration of rational maps on the Riemann sphere. It was founded in the claasical work by Fatou and Julia around 1918. After about 60 years of stagnation it was revived in the 1980s bringing together deep ideas of Conformal and Hyperbolic Geometry, Teichmuller Theory and Theory of Kleinian groups, Hyperbolic Dynamics and Ergodic Theory, and Renormalization Theory from physics, illustrated with beautiful computer pictures of fractal sets (like the Mandelbrot set). We will highlighten some landmarks of this story.