Extremely irradiated hot Jupiters, exoplanets reaching dayside temperatures >2000 K, stretch our understanding of planetary atmospheres and the models we use to interpret observations. While these objects are planets in every other sense, their atmospheres reach temperatures at low pressures comparable only to stellar atmospheres. In order to understand our a priori theoretical expectations for the nature of these objects, we self-consistently model a number of extreme hot Jupiter scenarios with the PHOENIX model atmosphere code. PHOENIX is well-tested on objects from cool brown dwarfs to expanding supernovae shells, and its expansive opacity database from the UV to far-IR make PHOENIX well-suited to understanding extremely irradiated hot Jupiters. We find several fundamental differences between hot Jupiters at temperatures >2500 K and their cooler counterparts. First, absorption by atomic metals like Fe and Mg, molecules including SiO and metal hydrides, and continuous opacity sources like H−, all combined with the short-wavelength output of early-type host stars, result in strong thermal inversions, without the need for TiO or VO. Second, many molecular species, including H2O, TiO, and VO are thermally dissociated at pressures probed by transit and eclipse observations, potentially biasing retrieval algorithms that assume uniform vertical abundances. We discuss other interesting properties of these objects, as well as future prospects and predictions for observing and characterizing this unique class of astrophysical object, including the first self-consistent model of the hottest known Jovian planet, KELT-9b.