A review of the most relevant aspects of fullerene electronic structure and spectroscopy is presented. Experimental data and their interpretation based on computational results are discussed both for fullerene C-60 and C-70, with particular attention to the properties of the isolated molecule. Concerning singlet state spectroscopy, it is shown that because of its high symmetry, only dipole-forbidden electronic states are found in the low excitation energy region of C-60. Conversely, the lowering of symmetry in C-70 leads to several complications in its electronic structure and spectroscopy, due to the presence of weakly allowed transitions in the low excitation energy region. A slightly less congested distribution of low lying excited states characterizes the triplet manifold of the fullerenes. It is concluded that while C-60 is important in aiding understanding of the main features in electronic spectroscopy of fullerenes, such as the presence of strong absorptions in the high energy range, its spectra are deeply influenced by its high symmetry and are very peculiar. On the other hand, C-70, with its lower symmetry and more complex spectra, represents a more realistic model for the intricate details of the electronic structure and electronic spectroscopy of larger and smaller fullerenes and their derivatives, which are generally characterized by lower symmetry compared to C-60.