Arc synthesis method, which is now the center for the synthesis of new carbon compounds such as carbon nanocapsules and carbon nanotubes, is introduced together with its current status. Many new carbon compounds are synthesized by DC arc discharge heating method (arc discharge method) in which a graphite bar is used as the electrode. C70 and higher order fullerenes having larger carbon numbers are found one after another in the soot produced by the arc discharge method, and the structures of C76, C78, C84, C90, C94, and others have been clarified. It is considered in the arc discharge method that the processes of a large amount of carbon evaporation by high temperature and the succeeding quenching cause to produce various kinds of new carbon compounds. In connection with other synthesis methods, synthesis of fullerenes by incomplete combustion, synthesis of nanotubes by the vapor phase thermal decomposition method, and the synthesis of nanotubes using casting molds are discussed. 24 refs., 6 figs.