This review describes five categories of the reactions of polycyclic aromatichydrocarbons, including photochemistry, electron attachment/detachment, recombinationprocesses, radical reactions, and ion-neutral chemistry. For each class of reaction, anoverview of the studies and their general results are presented, as well as references tothe literature. The thermochemistry of PAHs and relevant species is described, includingbond dissociation energies, ionization energies, electron affinities, basicities,acidities, and the interrelationships of these quantities. Modeling of the chemistry ofPAHs and their ions is discussed for both diffuse and dark clouds. The role of PAH cationsin the catalytic formation of molecular hydrogen is considered. Finally, this reviewconcludes with a discussion of current challenges in the chemical characterization ofPAHs, and a perspective for future studies.