The radiation from stars and active galactic nuclei (AGNs) creates photodissociation regions (PDRs) and X-ray-dominated regions (XDRs), where the chemistry or heating is dominated by far-ultraviolet (FUV) radiation or X-ray radiation, respectively. PDRs include a wide range of environments, from the diffuse interstellar medium (ISM) to dense star-forming regions. XDRs are found in the center of galaxies hosting AGNs, in protostellar disks, and in the vicinity of X-ray binaries. In this review, we describe the dominant thermal, chemical, and radiation transfer processes in PDRs and XDRs, as well as give a brief description of models and their use for analyzing observations. We then present recent results from Milky Way, nearby extragalactic, and high-redshift observations. Several important results include the following: ▪ Velocity-resolved PDR lines reveal the kinematics of the neutral atomic gas and provide constraints on the stellar feedback process. Their interpretation is, however, in dispute, as observations suggest a prominent role for stellar winds, whereas they are much less important in theoretical models. ▪ A significant fraction of molecular mass resides in CO-dark gas especially in low-metallicity and/or highly irradiated environments. ▪ The CO ladder and [Ci]/[Cii] ratios can determine if FUV or X rays dominate the ISM heating of extragalactic sources. ▪ With Atacama Large Millimeter/submillimeter Array, PDR and XDR tracers are now routinely detected on galactic scales over cosmic time. This makes it possible to link the star-formation history of the Universe to the evolution of the physical and chemical properties of the gas.