To date, chemical vapor deposition on transition metal catalysts is a potential way to achieve low cost, high quality and uniform wafer-scale graphene. However, the removal and transfer process of the annoying catalytic metals underneath can bring large amounts of uncertain factors causing the performance deterioration of graphene, such as the pollution of surface polymeric residues, unmentioned doping and structural damages. Thus, to develop a technique of directly fabricating graphene on dielectric substrates is quite meaningful. In this review, we will present specific methods of catalyst- or transfer-free techniques for graphene growth and discuss the diversity of growth mechanisms.