Controllable synthesis of large-scale and high-quality graphene film is a basis for development of electronic and spintronic devices. Chemical vapor deposition (CVD) has been considered as a potential method for the industrialized preparation of high-quality graphene. The substrate in CVD is used to support graphene and even help graphene grow. Different substrates may lead to different graphene growth results. Therefore, it is of great importance to select appropriate substrates and growth strategies. In addition, the performance demands of advanced device also urgently require high-quality CVD-derived graphene supports. In this review, we summarize the current advances in surface engineering on substrates for CVD growth of graphene. Surface engineering involves anisotropic disordered, anisotropic ordered, and isotropic homogeneous surfaces of catalytic substrates, and surfaces of insulating substrates. Meanwhile, we describe how to use different surface engineering techniques to control the orientation of graphene domains, grow large-area single-crystal graphene domains, and regulate graphene layers. This information will provide a reference for the effective selection of substrates. Moreover, we review the current progress of graphene in the fields of charge and spin transport, demonstrating that graphene has broad prospects in the next generation of communications and storage. Finally, the opportunities and challenges in the controllable CVD-derived preparation of graphene and its application are discussed.