Despite the promising future of lithium-oxygen (Li-O2) battery in replacing conventional lithium ion battery for high-energy applications, the complicated reaction mechanisms determining the sluggish discharge-charge kinetics have not been fully understood. Here, utilizing in situ liquid transmission electron microscopy, the (electro)chemical fundamentals in a working Li-O2 battery is explored. During discharge, the nucleation of Li2O2 is observed at the carbon electrode/electrolyte interface, and the following growth process exhibits Li+ diffusion-limited kinetics. Nucleation and growth of Li2O2 are also observed within the electrolyte, where there is no direct contact with the carbon electrode indicating the existence of non-Faradaic disproportionation reaction of intermediate LiO2 into Li2O2. The growth of Li2O2 isolated in the electrolyte exhibits O2 - diffusion-limited kinetics. Li2O2 at the carbon electrode surface and isolated in the electrolyte are both active upon charging and gradually decomposed. For Li2O2 particles rooted at the carbon electrode surface, the decomposition starts at the electrode/Li2O2 interface indicating electron-conduction limited charge kinetics. For Li2O2 isolated within the electrolyte, surprisingly, a side-to-side decomposition mode is identified indicating the non-Faradaic formation of dissolvable O2 -, whose diffusion in the electrolyte controls the overall charge kinetics. This work reveals further details of underlying mechanisms in a working Li-O2 battery and identifies various limiting factors controlling the discharge and charge processes.