A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, tube, and many other shapes. In this paper were considered works on formation and the synthesis of fullerenes in flames in the following sections, such as, the structure and properties of fullerenes; applications of fullerenes; methods for identification of fullerenes; methods for producing fullerenes; formation and synthesis of fullerenes in flame; synthesis of fullerenes in flames with applied electrical field; mechanism of fullerenes formation. Also was presented modified scheme for soot and fullerenes formation process in flames. It has been found that if the peripheral zone of the benzene flame is heated by some external source, such as a laser beam, which not just burns the soot but also creates the same conditions as in the middle of the flame, the concentration of fullerenes increases. The increase in the yield of fullerenes in the case where a ring electrode is positioned above the peripheral part of the reaction zone of a flame is due to the glow-discharge conditions providing an effective synthesis of fullerenes.