Recently developed chemical vapor deposition (CVD) is considered as an effective way to large-area and high-quality graphene preparation due to its ultra-low cost, high controllability, and high scalability. However, CVD-grown graphene film is polycrystalline, and composed of numerous grains separated by grain boundaries, which are detrimental to graphene-based electronics. Intensive investigations have been inspired on the controlled growth of graphene single crystals with the absence of intrinsic defects. As the two most concerned parameters, the size and morphology serve critical roles in affecting properties and understanding the growth mechanism of graphene crystals. Therefore, a precise tuning of the size and morphology will be of great significance in scale-up graphene production and wide applications. Here, recent advances in the synthesis of graphene single crystals on both metals and dielectric substrates by the CVD method are discussed. The review mainly covers the size and morphology engineering of graphene single crystals. Furthermore, recent progress in the growth mechanism and device applications of graphene single crystals are presented. Finally, the opportunities and challenges are discussed.