Graphene is the most broadly discussed and studied two-dimensional material because of its preeminent physical, mechanical, optical, and thermal properties. Until now, metal-catalyzed chemical vapor deposition (CVD) has been widely employed for the scalable production of high-quality graphene. However, in order to incorporate the graphene into electronic devices, a transfer process from metal substrates to targeted substrates is inevitable. This process usually results in contamination, wrinkling, and breakage of graphene samples - undesirable in graphene-based technology and not compatible with industrial production. Therefore, direct graphene growth on desired semiconductor and dielectric substrates is considered as an effective alternative. Over the past years, there have been intensive investigations to realize direct graphene growth using CVD methods without the catalytic role of metals. Owing to the low catalytic activity of non-metal substrates for carbon precursor decomposition and graphene growth, several strategies have been designed to facilitate and engineer graphene fabrication on semiconductors and insulators. Here, those developed strategies for direct CVD graphene growth on semiconductors and dielectrics for transfer-free fabrication of electronic devices are reviewed. By employing these methods, various graphene-related structures can be directly prepared on desired substrates and exhibit excellent performance, providing versatile routes for varied graphene-based materials fabrication.