Graphene is an important material with unique electronic properties. Aiming to obtain high quality samples at a large scale, graphene growth on metal surfaces has been widely studied. An important topic in these studies is the atomic scale growth mechanism, which is the precondition for a rational optimization of growth conditions. Theoretical studies have provided useful insights for understanding graphene growth mechanisms, which are reviewed in this article. On the mostly used Cu substrate, graphene growth is found to be more complicated than a simple adsorption-dehydrogenation-growth model. Growth on Ni surface is precipitation dominated. On surfaces with a large lattice mismatch to graphene, epitaxial geometry determin a robust nonlinear growth behavior. Further progresses in understanding graphene growth mechanisms is expected with intense theoretical studies using advanced simulation techniques, which will make a guided design of growth protocols practical.