Ab initio current densities induced by an external magnetic field have been computed for corannulene dianion, dication, and tetraanion. The pi-ring currents are found to be large with respect to benzene and to undergo remarkable changes in response to variations in the oxidation state. According to the results obtained here, the three corannulene ions plus the neutral species constitute a very special set that spans all of the possible patterns of rim and hub circulations: diatropic/hub-paratropic/rim (the dianion), paratropic/hub-paratropic/rim (the dication, assuming conformationally averaged current density), diatropic/hub-diatropic/rim (the tetraanion), and paratropic/hub-diatropic/rim (the neutral, as already reported by other authors). Orbital contributions and their breakdown into explicit contributions from virtual excitations have been analyzed. It is shown that the dianion and dication are both (2p) systems characterized by a single highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) rotationally allowed transition. For the dianion, this transition is responsible not only for the outer paratropic circulation but also for the inner diatropic circulation, a behavior that requires an extension of the few electron model based on orbital contributions to be fully rationalized. For the dication, the HOMO-LUMO transition provides a paratropic circulation localized on one indene subunit. However, because of the fast exchange of conformers, it is sensible to calculate an averaged current density field, which is characterized by con-rotating paratropic inner and outer ring currents. For the tetraanion, the calculated current pattern is in agreement with a previous indication, while the orbital analysis reveals that the HOMO and the HOMO - 1 contribute to both inner and outer circulations. Despite the small 6-31G** basis set employed to calculate current densities and magnetic properties, a satisfactory agreement between computed and available experimental (1)H and (13)C chemical shifts is found, providing a firm basis for the above conclusions. Remarkably, the "diamagnetic" corannulene dianion observed in NMR at low temperature is predicted to be a paramagnetic closed-shell species.