Worldwide efforts are being devoted to promote an efficient use of renewable energy sources and sustainable electric transportation. High efficiency energy conversion systems like batteries, which store/deliver high energy and power densities, are under development. While Li-ion batteries (LIBs) are the best performing batteries on the market and redox flow batteries are already used for stationary plants, a drastic step forward is needed to increase energy and power performance and decrease costs. Li/O-2 batteries are considered the next generation due to significantly higher energy delivery than LIBs. We demonstrate a radically new battery concept: a non-aqueous Li/O-2 battery that operates with a semisolid, flowable catholyte. The proof-of-concept is proven by a catholyte based on 2% wt. SuperP carbon dispersed in tetraethylene glycol dimethyl ether - lithium bis(trifluoromethane)sulfonimide. Oxygen redox reaction at the semi-solid catholyte is investigated by electrochemical, morphological and spectroscopic analyses. The perfomance of a semi-solid, flow Li/O-2 battery prototype operating at high discharge rates (up to 4 mA cm(-2)) with high discharge capacity (>175 mAh cm(-2)), energy (>500 mWh cm(-2)) and power (>7 mW cm(-2)) is reported. The strategies to approach the challenging target of 1 kWh kg(-1) and 2 kWh L-1 are also discussed. (c) 2016 Elsevier Ltd. All rights reserved.