This article describes the governing equations, computational algorithms, and other components entering into the Community Multiscale Air Quality (CMAQ) modeling system. This system has been designed to approach air quality as a whole by including state-of-the-science capabilities for modeling multiple air quality issues, including tropospheric ozone, fine particles, acid deposition, and visibility degradation. CMAQ was also designed to have multiscale capabilities so that separate models were not needed for urban and regional scale air quality modeling. By making CMAQ a modeling system that addresses multiple pollutants and different spatial scales, it has a “one-atmosphere” perspective that combines the efforts of the scientific community. To implement multiscale capabilities in CMAQ, several issues (such as scalable atmospheric dynamics and generalized coordinates), which depend on the desired model resolution, are addressed. A set of governing equations for compressible nonhydrostatic atmospheres is available to better resolve atmospheric dynamics at smaller scales. Because CMAQ is designed to handle scale-dependent meteorological formulations and a large amount of flexibility, its governing equations are expressed in a generalized coordinate system. This approach ensures consistency between CMAQ and the meteorological modeling system. The generalized coordinate system determines the necessary grid and coordinate transformations, and it can accommodate various vertical coordinates and map projections. The CMAQ modeling system simulates various chemical and physical processes that are thought to be important for understanding atmospheric trace gas transformations and distributions. The modeling system contains three types of modeling components (Models-3): a meteorological modeling system for the description of atmospheric states and motions, emission models for man-made and natural emissions that are injected into the atmosphere, and a chemistry-transport modeling system for simulation of the chemical transformation and fate. The chemical transport model includes the following process modules: horizontal advection, vertical advection, mass conservation adjustments for advection processes, horizontal diffusion, vertical diffusion, gas-phase chemical reactions and solvers, photolytic rate computation, aqueous-phase reactions and cloud mixing, aerosol dynamics, size distributions and chemistry, plume chemistry effects, and gas and aerosol deposition velocity estimation. This paper describes the Models-3 CMAQ system, its governing equations, important science algorithms, and a few application examples. This review article cites 114 references.