The accelerated production of sophisticated miniaturized mobile electronic devices, challenges such as the electrochemical propulsion of electric vehicles (EVs), and the need for large-scale storage of sustainable energy (i.e. load-levelling applications) motivate and stimulate the development of novel rechargeable batteries and super-capacitors. While batteries deliver high energy density but limited cycle life and power density, super-capacitors provide high power density and very prolonged cycling. Lithium-ion batteries are the focus of intensive R&D efforts because they promise very high energy density that may be suitable for electrical propulsion. Here, we review research on batteries with an emphasis on Li-ion battery technology, examining its suitability for EV applications. We also briefly examine other battery systems that may be of importance for load-levelling applications, including rechargeable magnesium batteries. We give a short review of the status of technologies beyond Li-ion batteries, including Li-sulfur and Li-oxygen systems. Finally, we briefly discuss recent progress in the R&D of advanced super-capacitors.