The recent launch of JWST is revolutionizing our understanding of exoplanet atmospheres by providing observations at an unprecedented level of detail. In this talk, I will discuss two methods for studying the atmospheres of exoplanets with JWST. First, I will discuss the potential for spectroscopic eclipse mapping with JWST. Spectroscopic eclipse mapping is the only observational technique which allows for simultaneous resolution of the atmosphere in three spatial dimensions: latitude, longitude, and altitude. I will present a spectroscopic eclipse map of the hot Jupiter WASP-18b, the first such map ever produced.
Second, I will present a method of using JWST to quickly determine which M dwarf planets host atmospheres through secondary eclipse observations. I will give an overview of the application of this method in the first two years of JWST science, including new, unpublished results from my own program to observe the hot terrestrial planet Gl 486b in secondary eclipse. Finally, I will briefly discuss synergies between JWST and upcoming extremely large telescopes in studying exoplanet atmospheres.