We assign the observed phosphorescence and high-resolution singlet-to-triplet absorption spectra of pyridine, performing large model vibronic coupling calculations involving six active modes and three near-degenerate electronic states, (3)A(1), (2)(3)A(1), and B-3(1). Vibronic coupling primarily through nu(8a) between (3)A(1) and (2)(3)A(1) results in the breakdown of the pseudo-parity selection rule: the lower surface has a double minimum, with each well corresponding to a diabatic single-determinant (pi,pi*) excitation. These states then strongly vibronically couple to B-3(1) primarily through nu(16b), resulting in a very complex (3)A' manifold. In addition, for the singlet manifold, we detail a low-lying conical intersection between B-1(1) and (1)A(2) and suggest that this intersection should have observable consequences for excited-state dynamics. These conclusions are obtained through the examination of all states below 5 eV in energy [B-1(1) (S-1), B-1(2) (S-2), (1)A(2) (S-3), (3)A(1), (2)(3)A(1), B-3(1), (3)A(2), and B-3(2)], performing CIS, CASSCF, CASPT2, CCSD, CCSD(T), EOM-CCSD, CNDO/S, B3LYP, BLYP, TD-B3LYP, and TD-BLYP calculations for the vertical excitation and emission energies; equilibrium, transition-stare, and conical-intersection structures; vibration frequencies; spin-orbit couplings; vibronic couplings; ESR atomic spin densities; and low-resolution absorption and emission band contours. Special techniques are developed for the application of the electronic structure methods to the evaluation of the required molecular properties, and it is shown that the application of a wide range of methods is required both because of the diversity of the required properties and because the intrinsic errors in the methods are of magnitudes that are chemically significant.