A magnesium-ion cell comprising (a) a cathode comprising a carbon or graphitic material as a cathode active material having a surface area to capture and store magnesium thereon, wherein the cathode forms a meso-porous structure having a pore size from 2 nm to 50 nm and a specific surface area greater than 50 m2/g; (b) an anode comprising an anode current collector alone or a combination of an anode current collector and an anode active material; (c) a porous separator disposed between the anode and the cathode; (d) electrolyte in ionic contact with the anode and the cathode; and (e) a magnesium ion source disposed in the anode to obtain an open circuit voltage (OCV) from 0.5 volts to 3.5 volts when the cell is made.