Understanding the global-scale dynamics of the chemical composition of our atmosphere is essential for addressing a wide range of environmental issues from air quality to climate change. Understanding this phenomenon enables us to evaluate and devise appropriate environmental policies, such as the Kyoto Protocol on global greenhouse gases emissions. Numerical modeling of global atmospheric chemical dynamics presents an enormous challenge associated with simulating hundreds of chemical species with time scales varying from milliseconds to years. In my talk, I will present an overview of the state of the art in global atmospheric chemistry modeling and will point out some of the mathematical challenges that need attention in this field.