All neutral atomic hydrogen gas and a large fraction of the molecular gas in the Milky Way Galaxy and external galaxies lie in PDRs, and PDRs are the origin of most of the nonstellar infrared (IR) and the millimeter CO emission from a galaxy. On the surfaces (A_v 1-3) of interstellar clouds, the absorption of far ultraviolet (FUV) photons (h_v 13.6 eV) by gas and dust grains leads to intense emission of [C II] 158 um, [O I] 63, 146 um, and H2 rovibrational transitions, as well as IR dust continuum and polycyclic aromatic hydrocarbon (PAH) emission features. Deeper in PDRs, CO rotational and [C I] 370, 609 um lines originate. The transition of H to H2 and C+ to CO occurs within PDRs. Theoretical models compared with observations diagnose such physical parameters as the density and temperature structure, the elemental abundances, and the FUV radiation field in PDRs. Applications include clouds next to H II regions, reflection nebulae, planetary nebulae, red giant outflows, circumstellar gas around young stars, diffuse clouds, the warm neutral medium (WNM), and molecular clouds in the interstellar radiation field: In summary, much of the interstellar medium in galaxies. This review focuses on dense PDRs in the Milky Way Galaxy. Theoretical PDR models help explain the observed correlation of the the CO J = 1-0 luminosity with the molecular mass and also suggest FUV-induced feedback mechanisms that may regulate star formation rates and the column density through giant molecular clouds.