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49 pags, 10 figs, 2 tabs. -- Supplementary data is available at the Publisher's web ; 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. ; A portion of the work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the NASA Aeronautics and Space Administration. A portion of the work was carried out the National Center for Atmospheric Research, which is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. PY acknowledges support from the Faculty of Science and Technology, Lancaster University. JB and UI acknowledge NordForsk under the Nordic Programme on Health and Welfare Project #75007: Understanding the link between air pollution and distribution of related health impacts and welfare in the Nordic countries (Nordic Welf Air); and the H2020-LCE project: Role of technologies in an energy efficient economy – model based analysis policy measures and transformation pathways to a sustainable energy system (REEEM), Grant agreement no.: 691739. GZ acknowledges the New Zealand Government's Strategic Science Investment Fund (SSIF) through the NIWA programme CACV. This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/N027736/1] and the Natural Environment Research Council [grant number NE/N003411/1]. ; Peer reviewed