We present an overview of what has been learned from nonlinear optical spectral studies in C-60 and C-70 by our group and others. These include third harmonic generation (THG), degenerate four-wave mixing (DFWM), and electroabsorption (EA). We present empirical models of interacting states consistent with spectra of EA, THG and DFWM in C-60 and C-70. The spectra in the dispersed and solid forms differ significantly. In C-60 the lowest-energy resonances in chi((3))(-omega; omega(1), omega(2), omega(3)) are dominated by ''forbidden'' transitions made allowed by vibronic coupling in the molecule and intermolecular coupling in the solid. These interactions must be included in theoretical models of C-60 if comparison is to be made between calculated and experimental nonlinear optical spectra. Major features of chi((3))spectra in C-70 can be modeled with Similar states redshifted from those of C-60.