Graphene, in its ideal form, is a two-dimensional (2D) material consisting of a single layer of carbon atoms arranged in a hexagonal lattice. The richness in morphological, physical, mechanical, and optical properties of ideal graphene has stimulated enormous scientific and industrial interest, since its first exfoliation in 2004. In turn, the production of graphene in a reliable, controllable, and scalable manner has become significantly important to bring us closer to practical applications of graphene. To this end, chemical vapor deposition (CVD) offers tantalizing opportunities for the synthesis of large-area, uniform, and high-quality graphene films. However, quite different from the ideal 2D structure of graphene, in reality, the currently available CVD-grown graphene films are still suffering from intrinsic defective grain boundaries, surface contaminations, and wrinkles, together with low growth rate and the requirement of inevitable transfer. Clearly, a gap still exits between the reality of CVD-derived graphene, especially in industrial production, and ideal graphene with outstanding properties. This Review will emphasize the recent advances and strategies in CVD production of graphene for settling these issues to bridge the giant gap. We begin with brief background information about the synthesis of nanoscale carbon allotropes, followed by the discussion of fundamental growth mechanism and kinetics of CVD growth of graphene. We then discuss the strategies for perfecting the quality of CVD-derived graphene with regard to domain size, cleanness, flatness, growth rate, scalability, and direct growth of graphene on functional substrate. Finally, a perspective on future development in the research relevant to scalable growth of high-quality graphene is presented.