The development of new rechargeable battery systems could fuel various energy applications, from personal electronics to grid storage. Rechargeable aluminium-based batteries offer the possibilities of low cost and low flammability, together with three-electron-redox properties leading to high capacity. However, research efforts over the past 30 years have encountered numerous problems, such as cathode material disintegration, low cell discharge voltage (about 0.55 volts ref. 5), capacitive behaviour without discharge voltage plateaus (1.1-0.2 volts or 1.8-0.8 volts) and insufficient cycle life (less than 100 cycles) with rapid capacity decay (by 26-85 per cent over 100 cycles). Here we present a rechargeable aluminium battery with high-rate capability that uses an aluminium metal anode and a three-dimensional graphitic-foam cathode. The battery operates through the electrochemical deposition and dissolution of aluminium at the anode, and intercalation/de-intercalation of chloroaluminate anions in the graphite, using a non-flammable ionic liquid electrolyte. The cell exhibits well-defined discharge voltage plateaus near 2 volts, a specific capacity of about 70 mA h g-1 and a Coulombic efficiency of approximately 98 per cent. The cathode was found to enable fast anion diffusion and intercalation, affording charging times of around one minute with a current density of ~4,000 mA g-1 (equivalent to ~3,000 W kg-1), and to withstand more than 7,500 cycles without capacity decay.