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Ground-based and spacecraft telescopic observations, combined with an intensive modeling effort, have greatly enhanced our understanding of hot giant planets and brown dwarfs over the past ten years. Although these objects are all fluid, hydrogen worlds with stratified atmospheres overlying convective interiors, they exhibit an impressive diversity of atmospheric behavior. Hot Jupiters are strongly irradiated, and a wealth of observations constrain the day-night temperature differences, circulation, and cloudiness. The intense stellar irradiation, presumed tidal locking and modest rotation leads to a novel regime of strong day-night radiative forcing. Circulation models predict large day-night temperature differences, global-scale eddies, patchy clouds, and, in most cases, a fast eastward jet at the equator-equatorial superrotation. The warm Jupiters may exhibit a wide range of rotation rates, obliquities, and orbital eccentricities, which, along with the weaker irradiation, leads to circulation patterns and observable signatures predicted to differ substantially from hot Jupiters. Brown dwarfs are typically isolated, rapidly rotating worlds; they radiate enormous energy fluxes into space and convect vigorously in their interiors. Their atmospheres exhibit patchiness in clouds and temperature on regional to global scales-the result of modulation by large-scale atmospheric circulation. Despite the lack of irradiation, such circulations can be driven by interaction of the interior convection with the overlying atmosphere, as well as self-organization of patchiness due to cloud-dynamical-radiative feedbacks. Finally, irradiated brown dwarfs help to bridge the gap between these classes of objects, experiencing intense external irradiation as well as vigorous interior convection. A hierarchy of modeling approaches have yielded major new insights into the dynamics governing these phenomena.