Abstract: Photochemical air quality models play a central role in both schentific investigation of how pollutants evlove in the atmosphere as well as developing policies to manage air quality. In the past 30 years, these models have evolved from rather crude representations of the physics and chemistry impacting trace species to their current state: comprehensive, but not complete. The evolution has included advancements in not only the level of process descriptions, but also the computational implementation, including numerical methods. As part of the NARSTO Critical Reviews, this article discusses the current strengths and weaknesses of air quality models and the modeling process. Current Eulerian models are found to represent well the primary processes impacting the evolution of trace species in most cases though some exceptions may exist. For example, sub-grid-scale processes, such as concentrated power plant plumes, are treated only approximately. It is not apparent how much such approximations affect their results and the polices based upon those results. A significant weakness has been in how investigators have addressed, and communicated, such uncertainties. Studies find that major uncertainties are due to model inputs, e.g., emissions and meteorology, more so than the model itself. One of the primary weakness identified is in the modeling process, not the models. Evaluation has been limited both due to data constraints. Seldom is there ample observational data to conduct a detailed model intercomparison using consistent data (e.g., the same emissions and meteorology). Further model advancement, and development of greater confidence in the use of models, is hampered by the lack of thorough evaluation and intercomparisons. Model advances are seen in the use of new tools for extending the interpretation of model results, e.g., process and sensitivity analysis, modeling systems to facilitate their use, and extension of model capabilities, e.g., aerosol dynamics capabilities and sub-grid-scale representations. Another possible direction that is the development and widespread use of a community model acting as a platform for multiple groups and agencies to collaborate and progress more rapidly.