As the most promising method for high quality, large area graphene synthesis, chemical vapor decomposition (CVD) has drawn enormous attention. Understanding of the growth mechanism is crucial for optimizing the experimental design to synthesize the desired graphene for various applications. Recently, many theoretical efforts have been devoted to explore the decomposition of feedstock, nucleation of small graphene islands, and the expansion of graphene islands to a large graphene sheet on various catalyst surfaces. Here we summarize the key progresses on the three aspects in order to provide a complete scenery of graphene CVD growth at the atomic level and to guide the experimental design for the synthesis of desired graphene, e. g., high quality graphene sheets with large single crystalline domains or controlled doping.