As one of the most appealing materials, graphene possesses remarkable electric, thermal, photoelectric and mechanic characteristics, which make it extremely valuable both for fundamental researches and practical applications. Nowadays the synthesis of graphene is commonly achieved by growing on metal substrate via chemical vapor deposition. For the integration in micro-electric device, the as-grown graphene needs to be transferred onto target dielectric layer. However, wrinkles, cracks, damages, and chemical residues from the metal substrate and the auxiliary polymer are inevitably introduced to graphene during such a transfer process, which are greatly detrimental to the performances of the graphene devices. Therefore, the direct synthesis of graphene on dielectric layer is of great importance. Many researches about this subject have been carried out in the last few years. While only few papers have systematically reviewed the direct growth of graphene on dielectric layer. For the in-depth understanding and further research of it, a detailed overview is required. In this paper, we summarize the recent research progress of the direct syntheses of graphene on dielectric layers, and expatiate upon different growth methods, including metal assisted growth, plasma enhanced growth, thermodynamics versus kinetics tailored growth, et al. Then differences in property between graphenes grown on various dielectric and insulating layers which serve as growth substrates in the direct growing process are discussed, such as SiO2/Si, Al2O3, SrTiO3, h-BN, SiC, Si3N4 and glass. Some kinds of mechanisms for graphene to be directly grown on dielectric layers have been proposed in different reports. Here in this paper, we review the possible growth mechanisms and divide them into van der Waals epitaxial growth and catalytic growth by SiC nanoparticles or oxygen atoms. Detailed data including Raman signals, sheet resistances, transmittances, carrier motilities are listed for the direct comparison of the quality among the graphenes grown on dielectric layers. The research focus and major problems existing in this field are presented in the last part of this paper. We also prospect the possible developing trend in the direct syntheses of high quality graphenes on dielectric layers in the future.