Single crystal graphene (SCG) has attracted enormous attention for its unique potential for next-generation high-performance optoelectronics. In the absence of grain boundaries, the exceptional intrinsic properties of graphene are preserved by SCG. Currently, chemical vapor deposition (CVD) has been recognized as an effective method for the large-scale synthesis of graphene films. However, polycrystalline films are usually obtained and the present grain boundaries compromise the carrier mobility, thermal conductivity, optical properties, and mechanical properties. The scalable and controllable synthesis of SCG is challenging. Recently, much attention has been attracted by the engineering of large-size single-crystal substrates for the epitaxial CVD growth of large-area and high-quality SCG films. In this article, a comprehensive and comparative review is provided on the selection and preparation of various single-crystal substrates for CVD growth of SCG under different conditions. The growth mechanisms, current challenges, and future development and perspectives are discussed.