Controllable growth of high quality, large area single-crystal graphene and bilayer graphene is critical for high-end applications in electronics and photonics. The discovery of graphene growth on copper by Chemical Vapor Deposition (CVD) has led to the polycrystalline large area films. In this talk, we presented two key mechanisms that are fundamentally important for graphene growth on Cu. (1) Oxygen (O) on the Cu surface substantially decreased the graphene nucleation density by passivating Cu surface active sites. Control of surface O enabled repeatable growth of centimeter-scale single-crystal graphene domains. O also accelerated graphene domain growth and shifted the growth kinetics from edge-attachment-limited to diffusion-limited. Correspondingly, the compact graphene domain shapes became dendritic. (2) We also established a new growth mechanism that can control the bernal-stacking ordering of two graphene layers, the synthesized single-crystal bilayer graphene domain can be as large as 500 micrometers, and more than 80% is of bernal stacking. Electrical transport property measurements also show carrier mobility over 60,000cm2v-1s-1 for both graphene and bilayer on Hexagonal Boron Nitride substrate. Particularly, we observed Bandgap ~100meV at a displacement field of 0.9V/nm in the CVD bilayer graphene, . Our works will meet the potentials of graphene in various applications.