As the first two-dimensional crystal isolated in 2004, graphene has triggered numerous fundamental and technological studies because of its unique properties and a wide range of potential applications. To take these applications to an industrial level requires successful large scale growth of high quality graphene. Among popular methods for graphene synthesis, chemical vapor deposition (CVD) has received a lot of attention because of its relatively high yields, high quality and low cost in preparation of graphene. In addition, CVD is compatible with the existing silicon semiconductor processes, and exhibits potential for synthesis and applications of graphene at industrial scale. CVD graphene has been synthesized on various metal substrates such as ruthenium, iridium, platinum, nickel and copper. Though suitable for mass production, the need to transfer the graphene to different substrates has so far constrained its up-scaling to roll-to-roll production methods. However, CVD graphene on metal need transfer to insulating substrates for further device fabrication and characterization, and the extra transfer step inevitably causes the degradation of the graphene quality because of crack formation or resists residues. Researchers have developed some novel technologies aiming at reducing the influence of transfer process on the quality of graphene, but transfer process is still time-consuming and relatively expensive. An alternative to overcome the transfer difficulty is to synthesize graphene directly on insulating substrates. Epitaxial growth of graphene on single crystal SiC is one route towards mass production of graphene, however, single crystal SiC wafers are still very expensive. The search for better production techniques of graphene, in particular a transfer-free production method of high quality graphene, has intensified over the last few years. An amount of effective strategies have been utilized to realize the direct synthesis of high quality graphene on insulating substrates such as h-BN, silicon oxide, quartz, sapphire, SrTiO3 and even normal glass. Due to the lack of catalytic capability and carbon-dissolving ability in insulating substrates, the direct growth of graphene often associates with the problems of high nucleation density, small domain size, poor layer control and slow growth rate. As such, more research works should be conducted to explore the growth mechanism on the insulating substrates. In this paper, we reviewed recent progresses about direct growth of graphene on insulating substrates by chemical vapor deposition and its electronic applications. Firstly, we briefly discussed the newly progresses of graphene preparation and application. Great progress have been achieved in the field of direct synthesis of graphene on insulating substrates, however, there is still much room to improve further in many aspects, such as quality, domain size, layer and substrate suitability of graphene. We classified the growth strategies on insulating substrates into four groups: non-catalyst assisted method, plasma enhanced method, interface catalyzed growth and metal-vapor assisted growth. In each strategy, details of technology and merits were carefully discussed. In addition, we also introduced the typical applications of each strategy, which exhibits extraordinary prospect for improving our daily life. Finally, we shared our perspective views on future trend of this research field. We believe that with more and more efforts from the graphene-research community, technologies about direct synthesis of graphene on insulating substrates will be developed further. The future of directly grown graphene will become clearer in industrial applications.