Graphene has emerged as the most popular topic in the active research field since graphene's discovery in 2004 by Andrei Geim and Kostya Novoselov. Since then, graphene research has exponentially accelerated because of its extraordinary properties, which have attracted the interest of researchers all over the world. For example, among the key properties are its thermal conductivity, electrical conductivity, optical transparency, and mechanical properties. These remarkable properties of graphene show its promise for applications in different industries including optical electronics, photovoltaic systems and others. However, the large-scale production and transfer method onto target substrates of monolayer graphene for commercial and industrial applications are still under study in the improvement stage. Therefore, this review presents the state-of-the-art research activities and latest advancement in the synthesis of graphene using various carbon precursors including solid, liquid and gas carbon feedstocks. The characterization methods have also been critically discussed in this review. In addition, the advancement in the transfer methods onto target substrates for achieving clean and high-quality transferred graphene have been thoroughly reviewed. Furthermore, the current growth mechanisms of single and multilayer graphene have also been discussed.