A comprehensive review of the state-of-the-art macroscopic modeling studies on lithium oxygen (Li O-2) and lithium air (Li air) batteries has been presented. The Li O-2 battery is a promising device for energy storage in portable electronics and electric vehicles due to its high specific energy. A number of technical challenges need to be addressed in order to bring this technology from laboratory concept to real products. The multi-scale, multi-physics phenomena in a Li O-2 battery encompasses a wide range of scientific disciplines, including electrochemistry, heat and mass transfer, and material science. Modeling study provides a powerful tool to understand the charge-species transport phenomena inside a battery that cannot be captured by experimentation. It offers insight to optimize battery design and fabrication. Macroscopic models that treat battery components as continuous media will be the focus of this review while pore-scale sub-models that are integrated with macroscopic models to describe structural changes of battery components (mainly electrodes) will be presented and compared as well. Recent developments and opportunities for future improvement and advancement are also discussed. Finally, a detailed summary of property data relevant to Li O-2 batteries is provided because of their critical role in modeling studies. (C) 2016 Elsevier B.V. All rights reserved.