Classical fullerenes are built of pentagonal and hexagonal rings, and the conventional syntheses produce only those isomers that obey the isolated-pentagon rule (IPR), where all pentagonal rings are separated from each other by hexagonal rings. Upon exohedral derivatization, the IPR fullerene cages normally retain their connectivity pattern. However, it has been discovered that high-temperature chlorination of fullerenes with SbCl5 or VCl4 can induce skeletal transformations that alter the carbon cage topology, as directly evidenced by single crystal X-ray diffraction studies of the chlorinated products of a series of fullerenes in the broad range of C60 to C102. Two general types of transformations have been identified: (i) the Stone-Wales rearrangement (SWR) that consists of a rotation of a C-C bond by 90°, and (ii) the removal of a C-C bond, i.e., C2 loss (C2L). Single- or multistep SWR and/or C2L transformations afford either classical non-IPR fullerenes bearing fused pentagons (highlighted in red in the TOC picture) or nonclassical (NCx) fullerenes with x = 1-3 heptagonal rings (highlighted in blue in the TOC picture) often flanked by fused pentagons. Several subtypes of the SWR and C2L processes can be further discerned depending on the local topology of the transformed region of the cage. Under the chlorination conditions, the non-IPR and NC carbon cages that would be energetically unfavorable and mostly labile in their pristine state are instantaneously stabilized by chlorination of the pentagon-pentagon junctions and by delimitation of the original spherical π-system into smaller favorable aromatic fragments. The significance of the chlorination-promoted skeletal transformations within the realm of fullerene chemistry is demonstrated by the growing body of examples. To date, these include single- and multistep SWRs in the buckminsterfullerene C60 and in the higher fullerenes C76(1), C78(2), C82(3), and C102(19), single and multistep C2Ls (i.e., cage shrinkage) in C86(16), C88(33), C90(28), C92(50), C96(80), C96(114), and C102(19), and multistep combinations of SWRs and C2Ls in C88(3), C88(33), and C100(18), (IPR isomer numbering in parentheses is according to the spiral algorithm). Remarkably, an IPR precursor can give rise to versatile transformed chlorinated fullerene cages formed via branched pathways. The products can be recovered either in their initial chlorinated form or as more soluble CF3/F derivatives obtained by an additional trifluoromethylation workup. Reconstruction of the skeletal transformation pathways is often complicated due to the lack of the isolable intermediate products in the multistep cases. Therefore, it is usually based on the principle of selecting the shortest pathways between the starting and the final cage. The quantum-chemical calculations illustrate the detailed mechanisms of the SWR and C2L transformations and the thermodynamic driving forces behind them. A particularly important aspect is the interplay between the chlorination patterns and the regiochemistry of the skeletal transformations.