Demand for better electric vehicles motivates the search for lower cost, higher capacity rechargeable batteries. The successful development of the rechargeable organic electrolyte lithium-air battery, which has received worldwide attention due to very high theoretical gravimetric energy density, is heavily dependent on the long-term stability of all battery components. In particular, finding organic aprotic solvents that are stable in the air cathode and allow the reversible formation and decomposition of lithium peroxide (Li2O2) as the only desired discharge product remains an elusive challenge. In this webinar, we present an overview of our research efforts directed towards identifying stable electrolyte compositions for Li-air systems from quantum chemical calculations. An integrated computational approach is developed that addresses different aspects of solvents stability in the air and lithium electrodes. This includes the susceptibility to nucleophilic substitution and proton abstraction by superoxide, autoxidation in the presence of molecular oxygen, and the ability to form a stable solid-electrolyte interphase on lithium metal. Computational screening of stable solvents can aid research into electrolyte systems that support long-term cycling in the lithium-air battery. Solvation phenomena play an important role in the cycling characteristics of the air electrode. We will also discuss theoretical models that can provide reliable description of solvation thermodynamics and complexation of Li+ and O2− ions and neutral lithium-oxygen compounds in organic solvents.