Employing the crossed-beams technique, we have studied the interaction of fullerene ions both with electrons and He2+ ions. For fullerene ions C60q+ (q = 1,2,3), absolute cross sections have been measured for C2-fragmentation at electron energies up to 1 keV. The cross sections for the loss of a C2 molecule indicate the presence of two different mechanisms. For negatively-charged fullerene ions Cm- (m = 60, 70, 84), absolute cross sections for multiple-ionization and fragmentation into product ions Cm-nq+ (q = 1,2,3 and n = 0,2,3) have been measured in the same range of electron energies. A novel ionization mechanism is proposed. In a very first ion-ion crossed-beams experiment involving fullerene ions, we have studied the charge transfer in collisions between C60+ ions and He2+ ions at keV energies. We have also calculated the total cross section for this reaction. Where the fullerene ion is described as an infinitely conducting hard sphere (ICS). The charge transfer S-matrix element was calculated as the electron transition coefficient over the time-dependent potential. For the calculation of the transition coefficients over a non-symmetric barrier, a new efficient method was developed.