The electronic spectra of the cation and anion of biphenyl have been studied using multiconfigurational second-order perturbation theory (CASPT2) and a basis set of ANO type, including polarization functions on the carbon atoms. For both cation and anion, two main transitions are obtained. The calculations for the cation give the intense vertical transitions placed at 1.9 and 3.2 eV in agreement with experimental evidence. A number of weak transitions are in addition found in the energy interval 1.1-4.6 eV. For the anion the strongest vertical transitions are calculated at 2.1 and 3.0 eV. The adiabatic electron affinity for biphenyl in the gas phase is computed to be -0.30 eV. The localized solutions obtained for the ground and excited states therefore correspond to shape resonances. The results are used for the interpretation of the polaron states of doped poly(paraphenylene). It is concluded that simple molecular orbital models used in earlier work do not give a proper description of the excitation process.