We discuss the idea of renormalization for complex dynamical systems. There various types of renormalizations defined via a first return map, appear in complex dynamics, for unimodal maps, homeomorphisms of circle, and germs of irrationally indifferent fixed points of holomorphic maps. The target of renormalization is usually tame and fragile dynamics and the connecting maps are often expanding maps and the exding property helps us to understand the rigid nature of the target maps. We propose the idea of dynamical charts for irrationally indifferent fixed points, in order to reconstruct the original map from the sequence of renormalizations.[-]