Graphene has attracted intense research interest due to its extraordinary properties and great application potential. Various methods have been proposed for the synthesis of graphene, among which chemical vapor deposition has drawn a great deal of attention for synthesizing large-area and high-quality graphene. Theoretical understanding of the synthesis mechanism is crucial for optimizing the experimental design for desired graphene production. In this review, we discuss the three fundamental steps of graphene synthesis in details, i.e. (1) decomposition of carbon feedstocks and formation of various active carbon species, (2) nucleation, and (3) attachment and extension. We provide a complete scenario of graphene synthesis on metal surfaces at atomistic level by means of density functional theory, molecular dynamics (MD), Monte Carlo (MC) and their combination and interface with other simulation methods such as quantum mechanical molecular dynamics, density functional tight binding molecular dynamics, and combination of MD and MC. We also address the latest investigation of the influences of the hydrogen and oxygen on the synthesis and the quality of the synthesized graphene.