We review several aspects of the calculation of exoplanet model atmospheres in the current era, with a focus on understanding the temperature-pressure profiles of atmospheres and their emitted spectra. Most of the focus is on gas giant planets, both under strong stellar irradiation and in isolation. The roles of stellar irradiation, metallicity, surface gravity, C/O ratio, interior fluxes, and cloud opacity are discussed. Connections are made to the well-studied atmospheres of brown dwarfs as well as sub-Neptunes and terrestrial planets, where appropriate. Illustrative examples of model atmosphere retrievals on a thermal emission spectrum are given and connections are made between atmospheric abundances and the predictions of planet formation models.
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