The PhotoDissociation Region Toolbox provides comprehensive, easy-to-use, public software tools and models that enable an understanding of the interaction of the light of young, luminous, massive stars with the gas and dust in the Milky Way and in other galaxies. It consists of an open-source Python toolkit and photodissociation region (PDR) models for analysis of infrared and millimeter/submillimeter line and continuum observations obtained by ground-based and suborbital telescopes, and astrophysics space missions. PDRs include all of the neutral gas in the interstellar medium where far-ultraviolet photons dominate the chemistry and/or heating. In regions of massive star formation, PDRs are created at the boundaries between the H II regions and neutral molecular cloud, as photons with energies 6 eV < hν < 13.6 eV photodissociate molecules and photoionize metals. The gas is heated by photoelectrons from small grains and large molecules and cools mostly through far-infrared (FIR) fine-structure lines like [O I] and [C II]. The models are created from state-of-the art PDR codes that include molecular freezeout; recent collision, chemical, and photorates; new chemical pathways, such as oxygen chemistry; and allow for both clumpy and uniform media. The models predict the emergent intensities of many spectral lines and FIR continuum. The tools find the best-fit models to the observations and provide insight into the physical conditions and chemical makeup of the gas and dust. The PDR Toolbox enables novel analysis of data from telescopes such as the Infrared Space Observatory, Spitzer, Herschel, the Stratospheric Terahertz Observatory, the Stratospheric Observatory for Infrared Astronomy, the Submillimeter Wave Astronomy Satellite, the Atacama Pathfinder Experiment, the Atacama Large Millimeter/submillimeter Array, and the JWST.