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The goal of the Tropospheric Ozone Assessment Report (TOAR) is to provide the research community with an up-to-date scientific assessment of tropospheric ozone, from the surface to the tropopause. While a suite of observations provides significant information on the spatial and temporal distribution of tropospheric ozone, observational gaps make it necessary to use global atmospheric chemistry models to synthesize our understanding of the processes and variables that control tropospheric ozone abundance and its variability. Models facilitate the interpretation of the observations and allow us to make projections of future tropospheric ozone and trace gas distributions for different anthropogenic or natural perturbations. This paper assesses the skill of current-generation global atmospheric chemistry models in simulating the observed present-day tropospheric ozone distribution, variability, and trends. Drawing upon the results of recent international multi-model intercomparisons and using a range of model evaluation techniques, we demonstrate that global chemistry models are broadly skillful in capturing the spatio-temporal variations of tropospheric ozone over the seasonal cycle, for extreme pollution episodes, and changes over interannual to decadal periods. However, models are consistently biased high in the northern hemisphere and biased low in the southern hemisphere, throughout the depth of the troposphere, and are unable to replicate particular metrics that define the longer term trends in tropospheric ozone as derived from some background sites. When the models compare unfavorably against observations, we discuss the potential causes of model biases and propose directions for future developments, including improved evaluations that may be able to better diagnose the root cause of the model-observation disparity. Overall, model results should be approached critically, including determining whether the model performance is acceptable for the problem being addressed, whether biases can be tolerated or corrected, whether the model is appropriately constituted, and whether there is a way to satisfactorily quantify the uncertainty.