Driven by the growing demand of energy storage devices, rechargeable LiÀO 2 batteries, especially non-aqueous ones, are considered as one of the most promising technologies due to their ultrahigh energy density. However, there are still many challenges, including poor catalytic activity, low conductivity and solvent degradation, to be overcome before their implementation in practical applications. Over decades, first-principles computations have made great progress and become a power-ful tool to predict key performances of various components in rechargeable LiÀO 2 batteries at atomic level. In this review, we introduce first-principles approaches, and summarize the recent advancement in computational investigations on cathode catalysts, products and solvents for rechargeable LiÀO 2 batteries. In addition, the challenges and potential research directions are also briefly discussed.