The last few years has seen a dramatic increase in the number of exoplanets known and in the range of methods for characterising their atmospheric properties. At the same time, new discoveries of increasingly cooler brown dwarfs have pushed down their temperature range which now extends down to Y-dwarfs of <300 K. Modelling of these atmospheres has required the development of new techniques to deal with the molecular chemistry and clouds in these objects. The atmospheres of brown dwarfs are relatively well understood, but some problems remain, in particular the behavior of clouds at the L/T transition. Observational data for exoplanet atmosphere characterization is largely limited to giant exoplanets that are hot because they are near to their star (hot Jupiters) or because they are young and still cooling. For these planets there is good evidence for the presence of CO and H2O absorptions in the IR. Sodium absorption is observed in a number of objects. Reflected light measurements show that some giant exoplanets are very dark, indicating a cloud free atmosphere. However, there is also good evidence for clouds and haze in some other planets. It is also well established that some highly irradiated planets have inflated radii, though the mechanism for this inflation is not yet clear. Some other issues in the composition and structure of giant exoplanet atmospheres such as the occurence of inverted temperature structures, the presence or absence of CO2 and CH4, and the occurrence of high C/O ratios are still the subject of investigation and debate.
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