This review describes the most significant published results devoted to the study of the nature of the higher fullerenes stability, revealing of correlations between the structural features of higher fullerene molecules and the possibility of their producing. A formalization of the substructure approach to assessing the stability of higher fullerenes is proposed, which is based on a detailed analysis of the main structural features of fullerene molecules. The developed substructure approach, together with the stability of the substructures constituting the fullerene molecule, helps to understand deeper the features of the electronic structure of fullerenes.
Keywords: higher fullerenes; overstrain; radical; stability; structure; substructure.