<p indent=0mm>In 2004, graphene was successfully prepared by micromechanical exfoliation of graphite, which attracts wide attention in the scientific research community. After that, related research of two-dimensional (2D) materials has received continuous exploration. In particular, academia and industry have paid tremendous attention and high expectations on graphene, owing to its remarkable and tunable physical, electrical, optical, magnetic properties and its potential applications in various fields. These practical applications include high performance electronics and optoelectronics, such as field effect transistors, transparent and flexible electrodes, spintronic devices, solar cells and so on. However, as is well-known, the practical commercial applications are based on mature and repeatable preparation of materials. Great achievements have been made in developing synthesis techniques, including micromechanical exfoliation, epitaxial growth, chemical vapor deposition (CVD), chemical exfoliation, arc discharge, segregation growth and bottom-up synthesis and so on. Among these methods, CVD method is regarded as the most versatile platform to obtain high quality, large area, and controllable number of layers with good repeatability and low cost for real commercial applications. Up to now, the past decade has witnessed significant developments in the field of CVD graphene synthesis. Herein, we present the development of this field by firstly introducing the origin of graphene and the background of CVD method. Then, the main achievements in the development of graphene since 2008 are presented from the point of view of controllable preparation. The CVD synthesis of graphene is focused mainly on four aspects: the selection and modification of catalytic substrates, the manipulation of reaction conditions, bandgap engineering and clean transfer. The selection of catalytic substrate plays a critical role in the controllable preparation of graphene by CVD method. The representative catalytic mechanisms of different substrates for growing graphene are introduced, followed by various modifications of catalytic metal substrates. Besides, surface morphology and microstructure of substrates have a great impact on the quality and uniformity of as-grown graphene. Thus, due to the disadvantages of non-uniform surface energy, defects, wrinkles and impurities on the surface of solid metal, the introduction of liquid copper catalytic system helps to better control the nucleation uniformity and optimize the graphene growth. Moreover, the preparation of large-area monocrystalline metal foils for obtaining large-scale single-crystal graphene was also reviewed. In order to avoid the disadvantages such as the damage, wrinkle and polymer pollution of graphene associated with transfer process occurred in the cases of using metal substrates to grow graphene, direct synthesis of graphene on dielectric substrates is presented with focuses on two basic controls of nucleation density and growth rate. A series of techniques such as reaction medium regulation, substrate surface modification, and plasma-assisted growth, the introduction of gaseous metals and direct preparation of graphene on liquid glass are introduced. The development of graphene vertical and planar heterostructures with hexagonal boron nitride is also presented. Moreover, the disadvantage of graphene limits its application in logic circuits due to its zero bandgap without an acceptable on/off ratio, and three main ways to open graphene bandgap are discussed including doping, the preparation of a large area of AB stacking bilayer graphene and engineering graphene nanoribbons. After that, a brief introduction of transfer method used in graphene post-processing is given. Finally, we summarize the problems existing in the field, and the future opportunities and challenges are discussed.