Large polycyclic aromatic hydrocarbon (PAH) molecules carry the infrared (IR) emission features that dominate the spectra of most galactic and extragalactic sources. This review surveys the observed mid-IR characteristics of these emission features and summarizes laboratory and theoretical studies of the spectral characteristics of PAHs and the derived intrinsic properties of emitting interstellar PAHs. Dedicated experimental studies have provided critical input for detailed astronomical models that probe the origin and evolution of interstellar PAHs and their role in the universe. The physics and chemistry of PAHs are discussed, emphasizing the contribution of these species to the photoelectric heating and the ionization balance of the interstellar gas and to the formation of small hydrocarbon radicals and carbon chains. Together, these studies demonstrate that PAHs are abundant, ubiquitous, and a dominant force in the interstellar medium of galaxies.