The chemical processes responsible for production of photochemical oxidants within the troposphere have been the subject of laboratory and field study throughout the last three decades. During the same period, models to simulate the atmospheric chemistry, transport and deposition of ozone (O(3)) from individual urban sources and from regions have been developed. The models differ greatly in the complexity of chemical schemes, in the underlying meteorology and in spatial and temporal resolution. Input information from land use, spatial and temporally disaggregated emission inventories and meteorology have all improved considerably in recent years and are not fully implemented in current models. The development of control strategies in both North America and Europe to close the gaps between current exceedances of environmental limits, guide values, critical levels or loads and full compliance with these limits provides the focus for policy makers and the support agencies for the research. The models represent the only method of testing a range of control options in advance of implementation. This paper describes currently applied models of photochemical oxidant production and transport at global and regional scales and their ability to simulate individual episodes as well as photochemical oxidant climatology. The success of current models in quantifying the exposure of terrestrial surfaces and the population to potentially damaging O(3) concentrations (and dose) is examined. The analysis shows the degree to which the underlying processes and their application within the models limit the quality of the model products.