In this tutorial review taking X-ray crystallographically characterized compounds as a starting point a walk is taken through the electronic and structural properties of endohedral metallofullerenes. After classification of the fullerenes according to the encapsulated guest, particular attention is given to identifying factors that determine the selection of a particular carbon cage network by the internal metal cluster. Some of the physical rules that determine which particular fullerene cage is formed will be discussed. Concepts such as charge transfer between the cage and the guest metal ions, the topology of the cage, the separations between the 12 pentagons on the fullerene surface, and the effect of entropic factors are used to rationalize the selection of a particular cage. The roles of electrochemistry and vibrational spectroscopy in combination with theoretical calculations are considered in understanding the structures of the endohedral fullerenes.