The radical cation of the polycyclic aromatic hydrocarbon pyrene has been formed by vapor-phase electron impact, trapped in an argon matrix at 12 K, and its visible and infrared spectra have been recorded. Integral intensities of both its electronic and vibrational bands have been determined. Comparison of the electronic absorption spectrum with previously reported argon- and neon-matrix-isolated spectra, vapor-phase photoelectron results, and multireference configuration interaction (MRCI) calculations by using the Pariser-Parr-Pople (PPP) approach and a new intermediate neglect of differential overlap (INDO) formalism, especially developed for spectroscopic purposes, shows good agreement. Theoretical frequencies and intensities of the vibrational modes have also been determined using a restricted Hartree-Fock treatment with a 3-21G split-valence basis set. Significant differences between the IR intensities of neutral and cationic pyrene are predicted and substantiated experimentally. Infrared absorption of perdeuterated pyrene radical cations has also been recorded and used to substantiate the proposed vibrational assignments.