Graphene has received many attentions from the scientist due to its outstanding properties since it was mechanically exfoliated. The rise of graphene has stimulated immense research on analogous two-dimensional (2D) materials, such as the hexagonal boron nitride (h-BN), monolayer transition metal dichalcogenides, black phosphorene, silicene, borophene and germanene. However, as a semimetal, gapless graphene has been limited in the application like semiconducting electronics. Previous theoretical calculations predict that a small bandgap will arise when the graphene is placed onto an h-BN substrate. Then graphene/h-BN (G/h-BN) lateral heterostructures have been fabricated by many research groups on metal substrates. Comparing vertical vdW layer assembling, the atomic G/h-BN system combining both the high carrier mobility and tunable bandgap can build in-plane integrated circuit directly. However, to reduce the interface scattering, a sharp atomic interface between graphene and h-BN is required. To date, some experiments have built high quality G/h-BN heterostructures with sharp atomic interfaces, while many others did not. The underlying growth mechanism is crucial to control the size and shapes of the G/h-BN heterostructures of high quality. In this review, we first review the growth mechanism of graphene, mainly focusing on the nucleating process, which plays a vital role to reduce the grain boundary in the overall growth. The nucleation behavior of graphene is influenced by the growth temperature, substrate, carbon source partial pressure and hydrogen partial pressure. We review the structure and energy evaluation of clusters in the graphene nucleation stage on the Ir(111) and Ni(111) surface. Moreover, the nucleation barrier and size can also be obtained by combing the first-principles calculations and classical nucleation theory. Secondly, we present an overview on experimental fabrication of G/h-BN heterojunctions. Up to now, lateral G/h-BN heterojunctions has been produced on some metal substrates such as Cu foil, Ru(0001), Rh(111), Ni(111), Ir(111) and Pt(111). There are several methods to construct G/h-BN heterojunctions in experiments which can be classified into two kinds: Batch chemical vapor deposition and two/multi-step growth. In the earlier period, the large area randomly hybridized h-BN and graphene are fabricated by this method through supplying C precursors and NH3-BH3 at the same time. Another routine is two/multi-step growth technique in which G/h-BN is deposited on a metal surface beforehand as seeds of the second step of growth. And afterwards, by alternating the type of source supply, in plane heterojunctions with the predeposited grains will be formed. The growth sequence is proved to be a crucial factor that determines the quality of heterostructures. For multistep growth, lithographically technology and etching process are introduced to get spatially controlled heterostructures. Then, we introduce recent studies on the growth mechanism of G/h-BN lateral heterostructure both by atomistic first-principles calculations and experimental observations. The heteroepitaxial growth of graphene along the predeposited h-BN domains is systematically investigated by classical nucleation theory. At the initial stage, C atoms tend to attach linearly along the B/N-edges rather than perpendicular to the edges which resemble the graphene growth on the metal surface. When the carbon concentration is low, the nucleation barriers of graphene at B/N-edges are lower compared to the case of a Cu terrace. Nevertheless, under high carbon concentration, the nucleation barriers and nucleation rates in the two cases become comparable. Therefore, the chemical potential of the carbon source should be controlled within a suitable range to produce high quality G/h-BN lateral heterostructures with sharply and continuously atomic interface. Finally, we give a prospect on this rising field.