The atmosphere of a brown dwarf or extrasolar giant planet controls the spectrum of radiation emitted by the object and regulates its cooling over time. Although the study of these atmospheres has been informed by decades of experience modeling stellar and planetary atmospheres, the distinctive characteristics of these objects present unique challenges to forward modeling. In particular, complex chemistry arising from molecule-rich atmospheres, molecular opacity line lists (sometimes running to 10 billion absorption lines or more), multiple cloud-forming condensates, and disequilibrium chemical processes all combine to create a challenging task for any modeling effort. This review describes the process of incorporating these complexities into one-dimensional radiative-convective equilibrium models of substellar objects. We discuss the underlying mathematics as well as the techniques used to model the physics, chemistry, radiative transfer, and other processes relevant to understanding these atmospheres. The review focuses on methods for creating atmosphere models and briefly presents some comparisons of model predictions to data. Current challenges in the field and some comments on the future conclude the review.


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