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Since the discovery of fullerenes, rapid development of their chemistry was observed primarily for C60 and C70. The chemistry of higher fullerenes with the number of carbon atoms more than 70 remains largely unexplored due to much less abundance in the fullerene soot and experimental difficulties in their isolation. Additional problems in isolation and characterization of higher fullerenes emerge because the number of possible cage isomers obeying the Isolated Pentagon Rule (IPR) is growing rapidly with the fullerene size. Separation of higher fullerenes is usually achieved by chromatographic methods (HPLC) accompanied by their characterization with 13C NMR spectroscopy, which is however not fully reliable in some cases. Derivatization of higher fullerenes followed by separation of derivatives and the use of direct methods for their characterization appeared to be rather effective as illustrated by several examples for C76 - C96. Reactions of a higher fullerenes mixture with CF3I or C2F5I followed by HPLC separation of perfluoroalkyl derivatives and their X-ray diffraction study allowed the characterization of cage connectivities of C76, C78 (two isomers), C82, C84 (six isomers), C86, C88, C92, C94, and C96. The use inorganic chlorides (SbCl5, VCl4, etc.) as chlorination agents resulted in isolation and crystallographic characterization of chlorides of C76, C78, and C90. Entirely new phenomena, skeletal transformations in the course of chemical reaction (chlorination), have been discovered by the examples of C76, C82, C86, and C88. Chlorination of IPR D2-C76 fullerene with SbCl5 is accompanied by a 7-step Stone-Wales skeletal rearrangement to non-IPR #18917C76Cl24 containing five pairs of fused pentagons in the carbon cage. Chlorination of isomer C86 (isomer 16) resulted in C84Cl32 with non-classical fullerene containing a heptagon in its cage. New skeletal rearrangements of C82 and C88 will be presented. The reasons of the skeletal rearrangements and their possible pathways are discussed in more detail.