To fabricate graphene based electronic and optoelectronic devices, it is highly desirable to develop a variety of metal‐catalyst free chemical vapor deposition (CVD) techniques for direct synthesis of graphene on dielectric and semiconducting substrates. This will help to avoid metallic impurities, high costs, time consuming processes, and defect‐inducing graphene transfer processes. Direct CVD growth of graphene on dielectric substrates is usually difficult to accomplish due to their low surface energy. However, a low‐temperature plasma enhanced CVD technique could help to solve this problem. Here, the recent progress of metal‐catalyst free direct CVD growth of graphene on technologically important dielectric (SiO2, ZrO2, HfO2, h‐BN, Al2O3, Si3N4, quartz, MgO, SrTiO3, TiO2, etc.) and semiconducting (Si, Ge, GaN, and SiC) substrates is reviewed. High and low temperature direct CVD growth of graphene on these substrates including growth mechanism and morphology is discussed. Detailed discussions are also presented for Si and Ge substrates, which are necessary for next generation graphene/Si/Ge based hybrid electronic devices. Finally, the technology development of the metal‐catalyst free direct CVD growth of graphene on these substrates is concluded, with future outlooks.