Plasma enhanced techniques are widely used for synthesis of carbon nanostructures. The primary focus of this paper is to summarize recent experimental and theoretical advances in understanding of single-wall carbon nanotube (SWNT) synthesis mechanism in arcs, and to describe methods of controlling arc plasma parameters. Fundamental issues related to synthesis of SWNTs, which is a relationship between plasma parameters and SWNT characteristics are considered. It is shown that characteristics of synthesized SWNTs can be altered by varying plasma parameters. Effects of electrical and magnetic fields applied during SWNT synthesis in arc plasma are explored. Magnetic field has a profound effect on the diameter, chirality, and length of a SWNT synthesized in the arc plasma. An average length of SWNT increases by a factor of 2 in discharge with magnetic field and an amount of long nanotubes with the length above 5 μm also increases in comparison with that observed in the discharge without a magnetic field. In addition, synthesis of a few-layer graphene in a magnetic field presence is discovered. A coupled model of plasma-electrode phenomena in atmospheric-pressure anodic arc in helium is described. Calculations indicate that substantial fraction of the current at the cathode is conducted by ions (0.7–0.9 of the total current). It is shown that nonmonotonic behavior of the arc current-voltage characteristic can be reproduced taking into account the experimentally observed dependence of the arc radius on arc current.