Spectroscopy of transiting exoplanets has revealed a wealth of information about their atmospheric compositions and thermal structures. In particular, studies of highly irradiated exoplanets at temperatures much higher than those found in our solar system have provided detailed information on planetary chemistry and physics because of the high level of precision which can be obtained from such observations. Here we use a variety of techniques to study the atmospheres of highly irradiated transiting exoplanets and address three large, open questions in exoplanet atmosphere spectroscopy. First, we use secondary eclipse and phase curve observations to investigate the thermal structures and heat redistribution of ultra-hot Jupiters, the hottest known exoplanets. We demonstrate how these planets form an unique class of objects influenced by high-temperature chemical effects such as molecular dissociation and H− opacity. Second, we use observations of helium in the upper atmosphere of the exo-Neptune HAT-P-11b to probe atmospheric escape processes. Third, we develop tools to interpret JWST observations of highly irradiated exoplanets, including a data analysis pipeline to perform eclipse mapping of hot Jupiters and a method to infer albedos of and detect atmospheres on hot, terrestrial planets. Finally, we discuss remaining open questions in the field of highly irradiated exoplanets and opportunities to advance our understanding of these unique bodies in the coming years.