Polycyclic aromatic hydrocarbons (PAHs) have been implicated as the carriers of the '' unidentified infrared'' (UIR) emission bands observed from the interstellar medium. It has long been thought that these molecules, if present, probably exist as cations. Laboratory-based spectra of the PAH cations in the visible and ultraviolet regions have been known for years, but comparable spectra in the infrared region have been lacking. In this paper we present infrared spectra of the cations of five moderate-sized PAHs. The PAH cations have been produced by low-energy electron impact and then trapped and stabilized in argon matrices at 12 K. To date, results have been obtained on naphthalene, anthracene, pyrene, perylene, and coronene. A common feature of the infrared spectra of all these cations is the very different intensity pattern of the ions compared to the neutral parents. Visible and (partial) infrared spectra of the coronene cation are also presented. It is shown that the out-of-plane CH bending mode shifts to a position very close to the UIR band at 11.3 mum. The astrophysical impact of these observations is discussed.