Arc discharge plasma is as one of the most practical and efficient methods to synthesize various carbon nanostructures such as single-walled carbon nanotubes (SWCNT) and graphene with minimal defects and large yield. This is achieved due to the relatively high synthesis temperature and eco-friendly growth mechanism. Moreover, by introducing a magnetic field during synthesis process, large-scale graphene and high-purity SWCNT can be obtained in one step. In addition, the yield of graphene can be controlled by external parameters, such as the type and pressure of buffer gas, the temperature of substrate, and plasma density and temperature. Bulk graphene (graphene platelets, flakes) is usually characterized by several layer (2-20 nm) graphene pieces having characteristics sizes of about microns to ten microns. Currently, the main method for synthesis of bulk graphene is chemical exfoliation, where chemicals are utilized to separate the graphene sheets from the piece of graphite. Current production capability are quite limited and estimated to be around several tens of tons of material annually worldwide. This work is focused on development of novel highly efficient and low cost plasma-based method for graphene production in industrial quantities characterized by exceptional product properties. The synthesis is based on utilization of arc discharge supported by ablation of anode material at atmospheric pressures. Pure carbon anode (several millimeters in diameter) and arc current in the range 50-100A were utilized for the synthesis. The graphene was synthesized on the metal substrate and was mechanically remove using metallic brush immediately after the synthesis. The synthesized samples were characterized using SEM, TEM and Raman spectroscopy. Typical size of the graphene platelets was found to be about several microns. The graphene platelets down to ~2 layers were obtained. We present state-of-the-art experimental data on various attempts to employ the arc plasma technique for the graphene synthesis and consider growth mechanisms including precipitation, surface-catalyzed processes and a substrate-independent approach. The potential of arc synthesis for the growth of other types of 2D materials and future prospects are discussed.