In this paper we investigate transport limitations in the electrodes of lithium-air batteries through computational modeling. We use meso-scale models to consider the effects of dendrites on the current and potential at the anode surface, and to investigate the effects of reaction and transport parameters on the formation of precipitates in the cathode. The formation of dendrites on the anode surface during cycling reduces the transport of ions and can lead to short circuits in the cell. Growth of precipitates in the cathode reduces the specific capacity of the cell due to surface passivation and pore clogging. Both of these degradation mechanisms depend on meso-scale phenomena, such as the porescale reactive transport in the cathode. To understand the effects of the meso-scale transport and precipitation on the performance and lifetime of Li-air batteries, meso-scale modeling is needed that is able to resolve the electrodes and their microstructures.