Each cell of a battery stores electrical energy as chemical energy in two electrodes, a reductant (anode) and an oxidant (cathode), separated by an electrolyte that transfers the ionic component of the chemical reaction inside the cell and forces the electronic component outside the battery. The output on discharge is an external electronic current I at a voltage V for a time Delta t. The chemical reaction of a rechargeable battery must be reversible on the application of a charging I and V. Critical parameters of a rechargeable battery are safety, density of energy that can be stored at a specific power input and retrieved at a specific power output, cycle and shelf life, storage efficiency, and cost of fabrication. Conventional ambient-temperature rechargeable batteries have solid electrodes and a liquid electrolyte. The positive electrode (cathode) consists of a host framework into which the mobile (working) cation is inserted reversibly over a finite solid solution range. The solid solution range, which is reduced at higher current by the rate of transfer of the working ion across electrode/electrolyte interfaces and within a host, limits the amount of charge per electrode formula unit that can be transferred over the time Delta t = Delta t(I). Moreover, the difference between energies of the LUMO and the HOMO of the electrolyte, i.e., electrolyte window, determines the maximum voltage for a long shelf and cycle life. The maximum stable voltage with an aqueous electrolyte is 1.5 V; the Li-ion rechargeable battery uses an organic electrolyte with a larger window, which increase the density of stored energy for a given Delta t. Anode or cathode electrochemical potentials outside the electrolyte window can increase V, but they require formation of a passivating surface layer that must be permeable to Li+ and capable of adapting rapidly to the changing electrode surface area as the electrode changes volume during cycling. A passivating surface layer adds to the impedance of the Li+ transfer across the electrode/electrolyte interface and lowers the cycle life of a battery cell. Moreover, formation of a passivation layer on the anode robs Li from the cathode irreversibly on an initial charge, further lowering the reversible Delta t. These problems plus the cost of quality control of manufacturing plague development of Li-ion rechargeable batteries that can compete with the internal combustion engine for powering electric cars and that can provide the needed low-cost storage of electrical energy generated by renewable wind and/or solar energy. Chemists are contributing to incremental improvements of the conventional strategy by investigating and controlling electrode passivation layers, improving the rate of Li+ transfer across electrode/electrolyte interfaces, identifying electrolytes with larger windows while retaining a Li+ conductivity sigma(Li) > 10(-3) S cm(-1), synthesizing electrode morphologies that reduce the size of the active particles while pinning them on current collectors of large surface area accessible by the electrolyte, lowering the cost of cell fabrication, designing displacement-reaction anodes of higher capacity that allow a safe, fast charge, and designing alternative cathode hosts. However, new strategies are needed for batteries that go beyond powering hand-held devices, such as using electrode hosts with two-electron redox centers; replacing the cathode hosts by materials that undergo displacement reactions (e.g. sulfur) by liquid cathodes that may contain flow-through redox molecules, or by catalysts for air cathodes; and developing a solid electrolyte separator membrane that allows an organic and aqueous liquid electrolyte on the anode and cathode sides, respectively. Opportunities exist for the chemist to bring together oxide and polymer or graphene chemistry in imaginative morphologies.