The discovery of exoplanets and the desire to understand their atmospheric chemical composition and habitability provides a new rationale for understanding the radiation from X-rays to radio wavelengths emitted by their host stars. Semiempirical models of stellar atmospheres that include accurate treatment of radiative transfer of all important atoms, ions, and molecules provide the essential basis for understanding a star's emitted radiation that is our main data source for characterizing a star and the radiation environment of its exoplanets. In Solar-type and cooler stars, the ultraviolet and extreme ultraviolet radiation formed in their chromospheres and transition regions drive the photochemistry in exoplanet atmospheres. In this review, I describe and critique the development of semiempirical static and time-dependent models of the chromospheres and transition regions of the Sun and cooler stars as well as the spectroscopic diagnostics upon which these models are based. The related topics of stellar coronae and winds and their theoretical bases are beyond the scope of this review.


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