The interstellar medium of galaxies is the reservoir out of which stars are born and into which stars inject newly created elements as they age. The physical properties of the interstellar medium are governed in part by the radiation emitted by these stars. Far-ultraviolet (6 eV less than h(nu) less than 13.6 eV) photons from massive stars dominate the heating and influence the chemistry of the neutral atomic gas and much of the molecular gas in galaxies. Predominantly neutral regions of the interstellar medium in which the heating and chemistry are regulated by far ultraviolet photons are termed Photo-Dissociation Regions (PDRs). These regions are the origin of most of the non-stellar infrared (IR) and the millimeter and submillimeter CO emission from galaxies. The importance of PDRs has become increasingly apparent with advances in IR and submillimeter astronomy. The IR emission from PDRs includes fine structure lines of C, C+, and O; rovibrational lines of H2, rotational lines of CO; broad middle features of polycyclic aromatic hydrocarbons; and a luminous underlying IR continuum from interstellar dust. The transition of H to H2 and C+ to CO occurs within PDRs. Comparison of observations with theoretical models of PDRs enables one to determine the density and temperature structure, the elemental abundances, the level of ionization, and the radiation field. PDR models have been applied to interstellar clouds near massive stars, planetary nebulae, red giant outflows, photoevaporating planetary disks around newly formed stars, diffuse clouds, the neutral intercloud medium, and molecular clouds in the interstellar radiation field-in summary, much of the interstellar medium in galaxies. Theoretical PDR models explain the observed correlations of the [CII] 158 microns with the COJ = 1-0 emission, the COJ = 1-0 luminosity with the interstellar molecular mass, and the [CII] 158 microns plus [OI] 63 microns luminosity with the IR continuum luminosity. On a more global scale, MR models predict the existence of two stable neutral phases of the interstellar medium, elucidate the formation and destruction of star-forming molecular clouds, and suggest radiation-induced feedback mechanisms that may regulate star formation rates and the column density of gas through giant molecular clouds.